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Significant figures

In math, numbers are exact by definition.

In science, numbers are usually from measurements, which are never exact.

How do let people know how accurate our measurements are?

We use significant figures” – Sig Figs

It’s just a simple way to let the reader know – using the decimal system – how accurate our measurements are.

Sig figs 2


the following is from


1. Zeroes placed before other digits are not significant:

0.0000023 only has 2 Significant figures.

2. Zeroes placed between other digits are always significant:

       5008 has 4 significant figures.

3. Zeroes placed after other digits, but behind a decimal point, are significant:

       2.90 has 3 significant figures.

 4. Zeroes at the end of a number are significant only if they are behind a decimal point, such as:  3.0    3.000


Decimals are necessary

Consider this number: 43000

Using the above rules, we can’t be sure how many sig figs there are.

How can we avoid ambiguity? Use scientific notation.

       4.300 x 10⁴     has 4 significant figures

       4.30 x 10⁴       has 3 significant figures

       4.3 x 10⁴         has 2 significant figures


Multiplying and Dividing

When multiplying or dividing, the # of sig figs should equal the least number of significant figures in any of the numbers used.


1. 3.0 m (2 sig figs) x 4.67 m (3 sig figs) = 14 (2 significant figures)

2. 3000.0 km (5 sig figs) / 6.0 km (2 sig fig)

= 500 X *The answer cannot be 500 because it must only have 2 sig figs.

so we put it into scienctific notation

= 5.0 x 10 to the 2.

Addition and subtraction

When adding or subtracting, the # of decimal places (not significant figures) in the answer should be the same as the least number of decimal places in any of the numbers used.


1. 3.98 (2 decimal places) + 4.3 (1 decimal place) + 4.66565632 (8 decimal places) = 12.9 ( 1 decimal place)

2. 39.00 (2 decimal place) – 5.543 (3 decimal places) + 3.33 (2 decimal places) = 36.79 (1 decimal place)

* Even though it may seem tempting to make this answer 36.8, you CANNOT because you must have 2 decimal places according to the data that you received.


When doing multi-step calculations, keep at least one more significant figure in intermediate results than needed in your final answer!
For example: If your intermediate step gets you with 2 sig figs add a 3rd so there is no error at the end.

External links

A Glossary of Frequently Misused or Misunderstood Physics Terms and Concepts.

Learning Standards

2016 Massachusetts Science Framework 2006

Physical Sciences (Chemistry and Physics) Grades 6-8

Recognize that the measurement of volume and mass requires understanding of the
sensitivity of measurement tools (e.g., rulers, graduated cylinders, balances) and
knowledge and appropriate use of significant digits.

The following skills are not detailed in the Mathematics Framework, but are necessary for a solid understanding in this course:
 Determine the correct number of significant figures.
 Determine percent error from experimental and accepted value

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