prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A stadimeter with a precision of +/- 20 meters measures a distance of 3630 meters and a measuring tape with a precision of +/- 0.4 meters reads 7.8 meters when measuring a distance between two different points. Using a calculator app, you multiply the numbers and get the output 28314.000000000000. When this output is reported to the proper number of significant digits, what do we get?
A. 28310 meters^2
B. 28000 meters^2
C. 28314.00 meters^2
D. 28314.000000000000 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A measuring tape with a precision of +/- 0.4 meters measures a distance of 0.1 meters and a balance with a precision of +/- 100 grams reads 683500 grams when measuring a mass. After multiplying the first value by the second value your computer yields the solution 68350.000000000000. If we express this solution to the appropriate number of significant digits, what is the answer?
A. 68350.0 gram-meters
B. 70000 gram-meters
C. 68300 gram-meters
D. 68350.000000000000 gram-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A measuring flask with a precision of +/- 0.002 liters measures a volume of 0.364 liters and a chronograph with a precision of +/- 0.3 seconds reads 6.4 seconds when measuring a duration. Using a calculator, you divide the first number by the second number and get the output 0.056875000000. When this output is expressed to the proper level of precision, what do we get?
A. 0.06 liters/second
B. 0.056875000000 liters/second
C. 0.057 liters/second
D. 0.1 liters/second
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A measuring stick with a precision of +/- 0.01 meters takes a measurement of 51.15 meters, and a stadimeter with a precision of +/- 4 meters reads 4251 meters when measuring a distance between two different points. You multiply the values with a calculator and get the solution 217438.650000000000. If we express this solution to the right number of significant digits, what is the result?
A. 217438.650000000000 meters^2
B. 217438 meters^2
C. 217400 meters^2
D. 217438.6500 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A measuring tape with a precision of +/- 0.3 meters takes a measurement of 9.6 meters, and a clickwheel with a precision of +/- 0.001 meters reads 5.452 meters when measuring a distance between two different points. Your calculator app gives the output 52.339200000000 when multiplying the two numbers. How would this answer look if we rounded it with the right number of significant digits?
A. 52.34 meters^2
B. 52.3 meters^2
C. 52.339200000000 meters^2
D. 52 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A cathetometer with a precision of +/- 0.0003 meters measures a distance of 0.9973 meters and an opisometer with a precision of +/- 0.001 meters measures a distance between two different points as 0.091 meters. After dividing the first value by the second value your computer produces the solution 10.959340659341. How can we round this solution to the right level of precision?
A. 11
B. 10.959
C. 10.959340659341
D. 10.96
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A stopwatch with a precision of +/- 0.004 seconds takes a measurement of 0.347 seconds, and a timer with a precision of +/- 0.02 seconds reads 0.07 seconds when measuring a duration of a different event. Using a calculator, you divide the first value by the second value and get the solution 4.957142857143. How would this answer look if we reported it with the appropriate number of significant digits?
A. 4.957142857143
B. 5.0
C. 5
D. 4.96
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

An analytical balance with a precision of +/- 4 grams measures a mass of 392 grams and an opisometer with a precision of +/- 0.002 meters reads 0.334 meters when measuring a distance. Your computer gives the output 130.928000000000 when multiplying the numbers. If we report this output to the right number of significant digits, what is the result?
A. 130.928000000000 gram-meters
B. 131 gram-meters
C. 130.928 gram-meters
D. 130 gram-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

An analytical balance with a precision of +/- 0.2 grams takes a measurement of 1.0 grams, and a storage container with a precision of +/- 0.1 liters reads 0.8 liters when measuring a volume. Your computer produces the output 1.250000000000 when dividing the former number by the latter. If we round this output to the right number of significant digits, what is the result?
A. 1.2 grams/liter
B. 1.250000000000 grams/liter
C. 1 grams/liter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

An analytical balance with a precision of +/- 0.0004 grams measures a mass of 0.5688 grams and a timer with a precision of +/- 0.004 seconds reads 8.384 seconds when measuring a duration. You divide the first value by the second value with a computer and get the output 0.067843511450. Express this output using the appropriate number of significant digits.
A. 0.067843511450 grams/second
B. 0.068 grams/second
C. 0.06784 grams/second
D. 0.0678 grams/second
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A radar-based method with a precision of +/- 200 meters measures a distance of 300 meters and a measuring stick with a precision of +/- 0.4 meters reads 793.0 meters when measuring a distance between two different points. Your calculator produces the output 237900.000000000000 when multiplying the two values. How would this answer look if we reported it with the correct level of precision?
A. 237900 meters^2
B. 237900.000000000000 meters^2
C. 200000 meters^2
D. 237900.0 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A tape measure with a precision of +/- 0.002 meters measures a distance of 0.010 meters and a clickwheel with a precision of +/- 0.003 meters reads 0.126 meters when measuring a distance between two different points. You divide the two values with a computer and get the solution 0.079365079365. How can we round this solution to the appropriate level of precision?
A. 0.079365079365
B. 0.079
C. 0.08
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A hydraulic scale with a precision of +/- 0.01 grams measures a mass of 3.36 grams and a meter stick with a precision of +/- 0.0002 meters measures a distance as 0.1450 meters. After multiplying the first number by the second number your computer produces the output 0.487200000000. How would this answer look if we reported it with the right level of precision?
A. 0.487 gram-meters
B. 0.49 gram-meters
C. 0.487200000000 gram-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A biltmore stick with a precision of +/- 0.03 meters measures a distance of 58.20 meters and a clickwheel with a precision of +/- 0.004 meters measures a distance between two different points as 0.007 meters. After dividing the numbers your calculator app gets the solution 8314.285714285714. When this solution is expressed to the appropriate level of precision, what do we get?
A. 8000
B. 8314.29
C. 8314.3
D. 8314.285714285714
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A caliper with a precision of +/- 0.002 meters measures a distance of 0.002 meters and a measuring tape with a precision of +/- 0.2 meters measures a distance between two different points as 32.7 meters. Using a calculator app, you multiply the first value by the second value and get the output 0.065400000000. If we report this output to the proper level of precision, what is the answer?
A. 0.1 meters^2
B. 0.065400000000 meters^2
C. 0.07 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A measuring tape with a precision of +/- 0.1 meters measures a distance of 44.1 meters and a chronometer with a precision of +/- 0.00001 seconds reads 0.08708 seconds when measuring a duration. You divide the numbers with a calculator and get the solution 506.430868167203. If we write this solution correctly with respect to the level of precision, what is the result?
A. 506.430868167203 meters/second
B. 506 meters/second
C. 506.4 meters/second
D. 506.431 meters/second
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A timer with a precision of +/- 0.002 seconds measures a duration of 1.227 seconds and a radar-based method with a precision of +/- 30 meters measures a distance as 1000 meters. After dividing the former value by the latter your computer gives the solution 0.001227000000. Report this solution using the suitable level of precision.
A. 0.001 seconds/meter
B. 0.00123 seconds/meter
C. 0.001227000000 seconds/meter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

An opisometer with a precision of +/- 1 meters takes a measurement of 2984 meters, and a stopwatch with a precision of +/- 0.4 seconds reads 501.8 seconds when measuring a duration. You multiply the first number by the second number with a computer and get the output 1497371.200000000000. Write this output using the correct number of significant digits.
A. 1497371 meter-seconds
B. 1497371.2000 meter-seconds
C. 1497000 meter-seconds
D. 1497371.200000000000 meter-seconds
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A spring scale with a precision of +/- 3000 grams takes a measurement of 5517000 grams, and a tape measure with a precision of +/- 0.004 meters reads 0.075 meters when measuring a distance. You multiply the numbers with a calculator and get the solution 413775.000000000000. Using the proper number of significant digits, what is the result?
A. 413000 gram-meters
B. 413775.00 gram-meters
C. 410000 gram-meters
D. 413775.000000000000 gram-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A tape measure with a precision of +/- 0.0004 meters takes a measurement of 0.0008 meters, and a stadimeter with a precision of +/- 200 meters measures a distance between two different points as 152500 meters. Your calculator app yields the output 122.000000000000 when multiplying the two numbers. How can we write this output to the proper number of significant digits?
A. 122.0 meters^2
B. 100 meters^2
C. 122.000000000000 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A clickwheel with a precision of +/- 0.04 meters measures a distance of 9.19 meters and a graduated cylinder with a precision of +/- 0.003 liters reads 3.111 liters when measuring a volume. Your calculator yields the solution 2.954034072645 when dividing the two numbers. How would this result look if we rounded it with the suitable number of significant digits?
A. 2.954034072645 meters/liter
B. 2.954 meters/liter
C. 2.95 meters/liter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A stopwatch with a precision of +/- 0.004 seconds measures a duration of 0.765 seconds and a coincidence telemeter with a precision of +/- 300 meters reads 249300 meters when measuring a distance. After multiplying the numbers your calculator gives the output 190714.500000000000. Using the appropriate level of precision, what is the answer?
A. 191000 meter-seconds
B. 190714.500000000000 meter-seconds
C. 190714.500 meter-seconds
D. 190700 meter-seconds
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A storage container with a precision of +/- 4 liters takes a measurement of 6 liters, and an opisometer with a precision of +/- 2 meters reads 24 meters when measuring a distance. You multiply the former value by the latter with a calculator app and get the solution 144.000000000000. Using the proper number of significant digits, what is the answer?
A. 144.000000000000 liter-meters
B. 144 liter-meters
C. 100 liter-meters
D. 144.0 liter-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

An analytical balance with a precision of +/- 0.4 grams measures a mass of 6.2 grams and a cathetometer with a precision of +/- 0.0001 meters measures a distance as 0.4231 meters. Using a computer, you multiply the numbers and get the output 2.623220000000. Express this output using the proper number of significant digits.
A. 2.62 gram-meters
B. 2.623220000000 gram-meters
C. 2.6 gram-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A chronometer with a precision of +/- 0.0003 seconds takes a measurement of 0.0379 seconds, and a chronograph with a precision of +/- 0.01 seconds measures a duration of a different event as 36.53 seconds. You multiply the former value by the latter with a calculator app and get the solution 1.384487000000. How would this result look if we wrote it with the right level of precision?
A. 1.384487000000 seconds^2
B. 1.384 seconds^2
C. 1.38 seconds^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A tape measure with a precision of +/- 0.004 meters takes a measurement of 7.418 meters, and a tape measure with a precision of +/- 0.003 meters measures a distance between two different points as 0.903 meters. Using a calculator, you divide the former number by the latter and get the output 8.214839424142. Express this output using the proper number of significant digits.
A. 8.215
B. 8.214839424142
C. 8.21
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A meter stick with a precision of +/- 0.0002 meters takes a measurement of 0.0891 meters, and a Biltmore stick with a precision of +/- 0.04 meters measures a distance between two different points as 0.37 meters. You multiply the numbers with a calculator and get the output 0.032967000000. Using the proper level of precision, what is the answer?
A. 0.03 meters^2
B. 0.032967000000 meters^2
C. 0.033 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A biltmore stick with a precision of +/- 0.2 meters takes a measurement of 61.4 meters, and a cathetometer with a precision of +/- 0.00001 meters measures a distance between two different points as 0.02470 meters. Using a calculator, you multiply the former value by the latter and get the solution 1.516580000000. If we write this solution to the appropriate level of precision, what is the result?
A. 1.5 meters^2
B. 1.517 meters^2
C. 1.52 meters^2
D. 1.516580000000 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A meter stick with a precision of +/- 0.0004 meters measures a distance of 0.0062 meters and a Biltmore stick with a precision of +/- 0.1 meters measures a distance between two different points as 1.5 meters. After multiplying the numbers your computer gives the output 0.009300000000. Using the appropriate level of precision, what is the result?
A. 0.01 meters^2
B. 0.009300000000 meters^2
C. 0.0093 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A clickwheel with a precision of +/- 0.2 meters takes a measurement of 343.6 meters, and a Biltmore stick with a precision of +/- 0.2 meters measures a distance between two different points as 28.8 meters. After multiplying the numbers your calculator app produces the output 9895.680000000000. If we express this output to the suitable level of precision, what is the result?
A. 9895.7 meters^2
B. 9895.680 meters^2
C. 9895.680000000000 meters^2
D. 9900 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A storage container with a precision of +/- 3 liters measures a volume of 5102 liters and a ruler with a precision of +/- 0.1 meters reads 29.3 meters when measuring a distance. After dividing the two numbers your computer gets the output 174.129692832765. If we round this output suitably with respect to the number of significant digits, what is the result?
A. 174 liters/meter
B. 174.129692832765 liters/meter
C. 174.130 liters/meter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A caliper with a precision of +/- 0.003 meters takes a measurement of 0.049 meters, and a hydraulic scale with a precision of +/- 1000 grams reads 4706000 grams when measuring a mass. Your calculator app gives the output 230594.000000000000 when multiplying the former value by the latter. How can we round this output to the correct level of precision?
A. 230000 gram-meters
B. 230594.00 gram-meters
C. 230594.000000000000 gram-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A tape measure with a precision of +/- 0.0001 meters takes a measurement of 0.0009 meters, and a tape measure with a precision of +/- 0.0001 meters measures a distance between two different points as 0.0007 meters. Using a calculator, you divide the former value by the latter and get the output 1.285714285714. How can we write this output to the proper number of significant digits?
A. 1.3
B. 1.2857
C. 1.285714285714
D. 1
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A balance with a precision of +/- 1 grams takes a measurement of 403 grams, and a measuring rod with a precision of +/- 0.004 meters reads 0.001 meters when measuring a distance. You divide the values with a calculator and get the output 403000.000000000000. Using the correct number of significant digits, what is the answer?
A. 403000.000000000000 grams/meter
B. 403000 grams/meter
C. 403000.0 grams/meter
D. 400000 grams/meter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A measuring tape with a precision of +/- 0.4 meters measures a distance of 0.2 meters and a chronograph with a precision of +/- 0.3 seconds measures a duration as 784.4 seconds. You multiply the first value by the second value with a computer and get the output 156.880000000000. How would this answer look if we reported it with the correct number of significant digits?
A. 200 meter-seconds
B. 156.880000000000 meter-seconds
C. 156.9 meter-seconds
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A balance with a precision of +/- 1 grams takes a measurement of 31 grams, and a measuring stick with a precision of +/- 0.3 meters measures a distance as 2.4 meters. Your calculator gets the solution 12.916666666667 when dividing the two values. If we express this solution properly with respect to the number of significant digits, what is the answer?
A. 12.916666666667 grams/meter
B. 12.92 grams/meter
C. 13 grams/meter
D. 12 grams/meter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A graduated cylinder with a precision of +/- 0.004 liters measures a volume of 0.377 liters and a stopwatch with a precision of +/- 0.02 seconds measures a duration as 0.12 seconds. Your calculator gets the output 0.045240000000 when multiplying the former number by the latter. If we write this output to the suitable level of precision, what is the result?
A. 0.05 liter-seconds
B. 0.045240000000 liter-seconds
C. 0.045 liter-seconds
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A biltmore stick with a precision of +/- 0.1 meters takes a measurement of 19.4 meters, and a stopwatch with a precision of +/- 0.1 seconds measures a duration as 888.5 seconds. Using a calculator, you multiply the two values and get the solution 17236.900000000000. Write this solution using the correct level of precision.
A. 17236.9 meter-seconds
B. 17236.900000000000 meter-seconds
C. 17236.900 meter-seconds
D. 17200 meter-seconds
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A graduated cylinder with a precision of +/- 0.002 liters takes a measurement of 0.800 liters, and a timer with a precision of +/- 0.04 seconds reads 0.05 seconds when measuring a duration. Using a calculator, you divide the former value by the latter and get the solution 16.000000000000. If we report this solution appropriately with respect to the number of significant digits, what is the answer?
A. 16.000000000000 liters/second
B. 20 liters/second
C. 16.00 liters/second
D. 16.0 liters/second
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A rangefinder with a precision of +/- 40 meters measures a distance of 5160 meters and a cathetometer with a precision of +/- 0.0004 meters measures a distance between two different points as 0.0949 meters. After dividing the two values your calculator app gets the output 54373.024236037935. Write this output using the right level of precision.
A. 54373.024236037935
B. 54370
C. 54400
D. 54373.024
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A spring scale with a precision of +/- 200 grams measures a mass of 7100 grams and a cathetometer with a precision of +/- 0.0004 meters measures a distance as 0.8261 meters. Your calculator app yields the output 8594.601137876770 when dividing the values. If we express this output appropriately with respect to the number of significant digits, what is the result?
A. 8594.601137876770 grams/meter
B. 8600 grams/meter
C. 8500 grams/meter
D. 8594.60 grams/meter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A measuring stick with a precision of +/- 0.001 meters measures a distance of 0.448 meters and a timer with a precision of +/- 0.3 seconds reads 7.6 seconds when measuring a duration. You multiply the first number by the second number with a computer and get the solution 3.404800000000. If we write this solution to the right number of significant digits, what is the answer?
A. 3.4 meter-seconds
B. 3.404800000000 meter-seconds
C. 3.40 meter-seconds
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A spring scale with a precision of +/- 30 grams takes a measurement of 95880 grams, and an opisometer with a precision of +/- 4 meters reads 891 meters when measuring a distance. After dividing the first number by the second number your calculator app gives the solution 107.609427609428. Using the right level of precision, what is the result?
A. 107.609427609428 grams/meter
B. 108 grams/meter
C. 100 grams/meter
D. 107.609 grams/meter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A tape measure with a precision of +/- 0.0004 meters measures a distance of 0.1162 meters and a timer with a precision of +/- 0.1 seconds measures a duration as 377.7 seconds. After dividing the first value by the second value your calculator app produces the solution 0.000307651575. How would this answer look if we reported it with the correct level of precision?
A. 0.0003 meters/second
B. 0.0003077 meters/second
C. 0.000307651575 meters/second
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

An odometer with a precision of +/- 3000 meters measures a distance of 4660000 meters and an odometer with a precision of +/- 4000 meters reads 8042000 meters when measuring a distance between two different points. Your computer yields the output 37475720000000.000000000000 when multiplying the first value by the second value. When this output is reported to the appropriate number of significant digits, what do we get?
A. 37475720000000.000000000000 meters^2
B. 37475720000000.0000 meters^2
C. 37480000000000 meters^2
D. 37475720000000 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A spring scale with a precision of +/- 0.4 grams takes a measurement of 7.0 grams, and a stadimeter with a precision of +/- 40 meters measures a distance as 300 meters. After dividing the first value by the second value your computer produces the output 0.023333333333. Report this output using the appropriate level of precision.
A. 0.023333333333 grams/meter
B. 0.023 grams/meter
C. 0.02 grams/meter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A measuring tape with a precision of +/- 0.3 meters measures a distance of 2.0 meters and a balance with a precision of +/- 3 grams measures a mass as 1334 grams. You multiply the former number by the latter with a calculator app and get the solution 2668.000000000000. How would this result look if we reported it with the appropriate level of precision?
A. 2700 gram-meters
B. 2668 gram-meters
C. 2668.000000000000 gram-meters
D. 2668.00 gram-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A spring scale with a precision of +/- 0.4 grams takes a measurement of 0.1 grams, and a spring scale with a precision of +/- 0.001 grams reads 0.007 grams when measuring a mass of a different object. Using a calculator app, you divide the former value by the latter and get the solution 14.285714285714. If we report this solution to the proper number of significant digits, what is the answer?
A. 14.285714285714
B. 10
C. 14.3
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A clickwheel with a precision of +/- 0.001 meters takes a measurement of 0.091 meters, and a chronograph with a precision of +/- 0.002 seconds measures a duration as 0.022 seconds. After multiplying the two numbers your computer yields the solution 0.002002000000. Using the correct number of significant digits, what is the result?
A. 0.002002000000 meter-seconds
B. 0.002 meter-seconds
C. 0.0020 meter-seconds
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A timer with a precision of +/- 0.04 seconds measures a duration of 13.68 seconds and a caliper with a precision of +/- 0.04 meters reads 6.68 meters when measuring a distance. After multiplying the former value by the latter your calculator yields the solution 91.382400000000. How would this result look if we expressed it with the correct number of significant digits?
A. 91.382 meter-seconds
B. 91.38 meter-seconds
C. 91.4 meter-seconds
D. 91.382400000000 meter-seconds
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A measuring stick with a precision of +/- 0.3 meters takes a measurement of 0.1 meters, and a storage container with a precision of +/- 2 liters measures a volume as 84 liters. Your computer gives the solution 8.400000000000 when multiplying the values. If we write this solution properly with respect to the number of significant digits, what is the answer?
A. 8.4 liter-meters
B. 8 liter-meters
C. 8.400000000000 liter-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A measuring flask with a precision of +/- 0.003 liters measures a volume of 1.362 liters and a ruler with a precision of +/- 0.0001 meters measures a distance as 0.2387 meters. Your calculator app produces the output 0.325109400000 when multiplying the two values. If we round this output correctly with respect to the number of significant digits, what is the result?
A. 0.325109400000 liter-meters
B. 0.3251 liter-meters
C. 0.325 liter-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A stadimeter with a precision of +/- 2 meters takes a measurement of 6 meters, and a balance with a precision of +/- 20 grams measures a mass as 30 grams. Your calculator app gets the output 180.000000000000 when multiplying the values. How can we report this output to the proper number of significant digits?
A. 180.0 gram-meters
B. 200 gram-meters
C. 180 gram-meters
D. 180.000000000000 gram-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A biltmore stick with a precision of +/- 0.01 meters measures a distance of 2.50 meters and a clickwheel with a precision of +/- 0.1 meters measures a distance between two different points as 9.5 meters. You divide the two numbers with a computer and get the solution 0.263157894737. Write this solution using the suitable level of precision.
A. 0.263157894737
B. 0.3
C. 0.26
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

An opisometer with a precision of +/- 0.0001 meters takes a measurement of 0.0067 meters, and a spring scale with a precision of +/- 300 grams measures a mass as 94900 grams. You multiply the numbers with a calculator and get the output 635.830000000000. Express this output using the correct level of precision.
A. 600 gram-meters
B. 635.83 gram-meters
C. 635.830000000000 gram-meters
D. 640 gram-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A clickwheel with a precision of +/- 0.2 meters takes a measurement of 833.9 meters, and a coincidence telemeter with a precision of +/- 4 meters measures a distance between two different points as 605 meters. Using a computer, you multiply the first value by the second value and get the output 504509.500000000000. How would this answer look if we rounded it with the right number of significant digits?
A. 504509.500000000000 meters^2
B. 504509 meters^2
C. 505000 meters^2
D. 504509.500 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A meter stick with a precision of +/- 0.0004 meters measures a distance of 0.0369 meters and an opisometer with a precision of +/- 0.0001 meters reads 0.0015 meters when measuring a distance between two different points. Using a calculator app, you divide the two numbers and get the output 24.600000000000. How can we write this output to the appropriate number of significant digits?
A. 24.600000000000
B. 24.60
C. 24.6000
D. 25
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A graduated cylinder with a precision of +/- 0.004 liters takes a measurement of 0.065 liters, and a chronograph with a precision of +/- 0.02 seconds reads 0.01 seconds when measuring a duration. Using a calculator, you divide the numbers and get the output 6.500000000000. How can we report this output to the correct level of precision?
A. 6.50 liters/second
B. 6.5 liters/second
C. 6.500000000000 liters/second
D. 6 liters/second
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A ruler with a precision of +/- 0.0001 meters measures a distance of 0.7607 meters and an analytical balance with a precision of +/- 2 grams reads 15 grams when measuring a mass. After dividing the values your computer gives the solution 0.050713333333. How can we report this solution to the right number of significant digits?
A. 0.05 meters/gram
B. 0.051 meters/gram
C. 0.050713333333 meters/gram
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

An analytical balance with a precision of +/- 400 grams measures a mass of 927500 grams and a storage container with a precision of +/- 1 liters reads 4 liters when measuring a volume. You divide the two numbers with a calculator app and get the output 231875.000000000000. When this output is reported to the right level of precision, what do we get?
A. 200000 grams/liter
B. 231800 grams/liter
C. 231875.0 grams/liter
D. 231875.000000000000 grams/liter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A timer with a precision of +/- 0.01 seconds takes a measurement of 0.76 seconds, and a stadimeter with a precision of +/- 0.2 meters measures a distance as 4.4 meters. Your computer produces the output 0.172727272727 when dividing the two numbers. How would this result look if we reported it with the proper number of significant digits?
A. 0.17 seconds/meter
B. 0.2 seconds/meter
C. 0.172727272727 seconds/meter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A chronograph with a precision of +/- 0.4 seconds measures a duration of 8.6 seconds and a clickwheel with a precision of +/- 0.01 meters reads 70.05 meters when measuring a distance. You divide the former number by the latter with a calculator app and get the output 0.122769450393. If we write this output properly with respect to the level of precision, what is the answer?
A. 0.12 seconds/meter
B. 0.122769450393 seconds/meter
C. 0.1 seconds/meter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A stopwatch with a precision of +/- 0.01 seconds measures a duration of 0.05 seconds and a radar-based method with a precision of +/- 40 meters reads 850 meters when measuring a distance. After multiplying the numbers your computer produces the output 42.500000000000. When this output is reported to the right level of precision, what do we get?
A. 42.500000000000 meter-seconds
B. 40 meter-seconds
C. 42.5 meter-seconds
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A coincidence telemeter with a precision of +/- 2 meters takes a measurement of 776 meters, and a chronograph with a precision of +/- 0.001 seconds reads 0.053 seconds when measuring a duration. Using a computer, you divide the first number by the second number and get the output 14641.509433962264. When this output is rounded to the suitable level of precision, what do we get?
A. 14641 meters/second
B. 14641.509433962264 meters/second
C. 14641.51 meters/second
D. 15000 meters/second
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A balance with a precision of +/- 0.4 grams measures a mass of 975.3 grams and a balance with a precision of +/- 0.01 grams reads 3.82 grams when measuring a mass of a different object. You multiply the first value by the second value with a calculator and get the output 3725.646000000000. Round this output using the right level of precision.
A. 3725.646 grams^2
B. 3725.6 grams^2
C. 3730 grams^2
D. 3725.646000000000 grams^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A biltmore stick with a precision of +/- 0.2 meters takes a measurement of 59.4 meters, and a storage container with a precision of +/- 2 liters measures a volume as 8416 liters. Using a computer, you multiply the former number by the latter and get the solution 499910.400000000000. When this solution is rounded to the suitable number of significant digits, what do we get?
A. 499910 liter-meters
B. 500000 liter-meters
C. 499910.400000000000 liter-meters
D. 499910.400 liter-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

An opisometer with a precision of +/- 0.004 meters takes a measurement of 9.154 meters, and a stopwatch with a precision of +/- 0.03 seconds reads 36.10 seconds when measuring a duration. Using a computer, you multiply the first number by the second number and get the solution 330.459400000000. If we express this solution to the suitable level of precision, what is the answer?
A. 330.5 meter-seconds
B. 330.459400000000 meter-seconds
C. 330.4594 meter-seconds
D. 330.46 meter-seconds
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A caliper with a precision of +/- 0.02 meters measures a distance of 0.56 meters and a measuring stick with a precision of +/- 0.04 meters measures a distance between two different points as 0.44 meters. Your calculator gets the solution 1.272727272727 when dividing the two values. Using the right level of precision, what is the answer?
A. 1.3
B. 1.27
C. 1.272727272727
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A clickwheel with a precision of +/- 0.02 meters takes a measurement of 51.78 meters, and a ruler with a precision of +/- 0.3 meters reads 29.6 meters when measuring a distance between two different points. You multiply the two numbers with a calculator and get the output 1532.688000000000. Round this output using the proper level of precision.
A. 1532.688 meters^2
B. 1530 meters^2
C. 1532.7 meters^2
D. 1532.688000000000 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A chronograph with a precision of +/- 0.04 seconds takes a measurement of 9.53 seconds, and a measuring rod with a precision of +/- 0.0004 meters measures a distance as 0.3917 meters. After dividing the numbers your calculator produces the output 24.329844268573. If we express this output suitably with respect to the number of significant digits, what is the result?
A. 24.33 seconds/meter
B. 24.3 seconds/meter
C. 24.330 seconds/meter
D. 24.329844268573 seconds/meter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

An analytical balance with a precision of +/- 0.4 grams measures a mass of 408.9 grams and a measuring rod with a precision of +/- 0.0004 meters reads 0.9560 meters when measuring a distance. Using a calculator app, you divide the values and get the solution 427.719665271967. Express this solution using the appropriate level of precision.
A. 427.719665271967 grams/meter
B. 427.7197 grams/meter
C. 427.7 grams/meter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

An opisometer with a precision of +/- 0.4 meters measures a distance of 14.4 meters and a spring scale with a precision of +/- 0.004 grams measures a mass as 0.098 grams. Your calculator gets the solution 1.411200000000 when multiplying the former value by the latter. When this solution is expressed to the correct level of precision, what do we get?
A. 1.4 gram-meters
B. 1.411200000000 gram-meters
C. 1.41 gram-meters
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A coincidence telemeter with a precision of +/- 40 meters takes a measurement of 20 meters, and a meter stick with a precision of +/- 0.0002 meters reads 0.0028 meters when measuring a distance between two different points. You multiply the two values with a calculator app and get the solution 0.056000000000. If we report this solution suitably with respect to the level of precision, what is the result?
A. 0.056000000000 meters^2
B. 0.1 meters^2
C. 0.06 meters^2
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

A chronograph with a precision of +/- 0.01 seconds takes a measurement of 0.06 seconds, and a meter stick with a precision of +/- 0.0001 meters reads 0.0088 meters when measuring a distance. After dividing the first value by the second value your calculator yields the output 6.818181818182. How would this result look if we rounded it with the correct level of precision?
A. 7 seconds/meter
B. 6.8 seconds/meter
C. 6.82 seconds/meter
D. 6.818181818182 seconds/meter
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
---

An opisometer with a precision of +/- 0.04 meters takes a measurement of 0.10 meters, and a hydraulic scale with a precision of +/- 0.0002 grams measures a mass as 0.0002 grams. Your computer produces the solution 500.000000000000 when dividing the first value by the second value. How would this answer look if we wrote it with the correct level of precision?
A. 500 meters/gram
B. 500.0 meters/gram
C. 500.000000000000 meters/gram
D. 500.00 meters/gram
Answer:


prompt:
NOTE: To propagate uncertainty when multiplying or dividing two measurements, count the number of significant digits in each. Your result should be reported to the number of significant digits in the measurement having the lesser number of significant digits. Note that 'significant digits' are different than 'decimal places'; see rules at https://en.wikipedia.org/w/index.php?title=Significant_figures&oldid=1114415444#Identifying_significant_figures .
Rounding a number to N significant digits is similar to rounding to N digits after the decimal point, except that we start counting from the beginning of the number. For example, 71.25150 rounded to three significant digits is 71.3, to four is 71.25, and to one is 70. (If the N + 1 digit is 5 followed by nothing or by zeros only, use the 'round half to even' tiebreaking rule).
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A measuring stick with a precision of +/- 0.03 meters takes a measurement of 0.30 meters, and a measuring tape with a precision of +/- 0.02 meters measures a distance between two different points as 0.24 meters. Your calculator produces the output 0.072000000000 when multiplying the former number by the latter. If we round this output to the right number of significant digits, what is the result?
A. 0.07 meters^2
B. 0.072000000000 meters^2
C. 0.072 meters^2
Answer: