section_path: Arithmetic with fractions/Converting between decimals and fractions
section_name: Converting between decimals and fractions
paragraph_text: Converting between decimals and fractions
  
  To change a common fraction to a decimal, do a long division of the decimal representations of the numerator by the denominator (this is idiomatically also phrased as "divide the denominator into the numerator"), and round the answer to the desired accuracy. For example, to change 1 / 4 to a decimal, divide 1.00 by 4 (" 4 into 1.00 "), to obtain 0.25. To change 1 / 3 to a decimal, divide 1.000... by 3 (" 3 into 1.000... "), and stop when the desired accuracy is obtained, e.g., at 4 decimals with 0.3333. The fraction 1 / 4 can be written exactly with two decimal digits, while the fraction 1 / 3 cannot be written exactly as a decimal with a finite number of digits. To change a decimal to a fraction, write in the denominator a 1 followed by as many zeroes as there are digits to the right of the decimal point, and write in the numerator all the digits of the original decimal, just omitting the decimal point. Thus 12.3456 = 123456 10000. {\displaystyle 12.3456={\tfrac {123456}{10000}}.}