Fraction to Decimal Converter

How to convert a fraction to a decimal

A fraction is a division in disguise: the bar means "divided by". To turn 3/8 into a decimal, divide 3 by 8 and you get 0.375. For a mixed number, convert it to an improper fraction first (2 1/4 = 9/4) or simply add the whole part to the decimal of the fractional part (2 + 0.25). The converter handles both routes automatically: use the optional whole-number field and it does the rest, shows the percent equivalent, and prints each step of the working so you can copy it into homework.

Because the division is carried out with exact integer long division instead of floating-point numbers, you get every digit right, even for fractions with large denominators. Results are limited to 60 decimal places; when a decimal is cut off at that point it ends with an ellipsis.

Terminating and repeating decimals

Some fractions end after a few digits (1/4 = 0.25) and others never do (1/3 = 0.333…). The rule is simple: reduce the fraction, then look at the denominator. If its only prime factors are 2 and 5, the decimal terminates, because those are the factors of 10. Any other prime factor, like 3 or 7, forces the digits to repeat. The repeating block can be long: 1/7 repeats the six digits 142857. This tool writes the repeating part in parentheses, so 1/7 appears as 0.(142857) and 1/6 as 0.1(6).

Handy values to remember: 1/2 = 0.5, 1/3 = 0.(3), 1/4 = 0.25, 1/5 = 0.2, 1/8 = 0.125 and 3/4 = 0.75. For the opposite direction use the decimal to fraction converter, and for percentages try the percent to fraction converter. All calculations run locally in your browser.