Fraction to Decimal Calculator: Exact, Rounded and Percent
Turn any fraction or mixed number into its exact decimal, with the repeating digits marked, plus the value rounded to the places you need and as a percent.
Divide the numerator by the denominator. 3/8 means 3 divided by 8, which is 0.375, or 37.5%. Some fractions never end: 2/3 becomes 0.666..., with the 6 repeating forever, written here as 0.(6), and rounded to four places it is 0.6667.
This calculator converts fractions to decimals in your browser for general use. Results are exact apart from the rounding you choose and the 60-digit cut on very long repeating blocks. Check the place count your teacher, form or software expects before copying a rounded value.
Leave the whole box blank for a plain fraction. A minus sign goes on the whole number or, with no whole number, on the numerator. Rounding takes 0 to 20 places.
Exact decimal
0.375
Terminates after 3 digits
- In lowest terms
- 3/8
- Rounded to 4 places
- 0.3750
- As a percent
- 37.5%
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About the Fraction to Decimal Calculator
A fraction is already a division, so its decimal comes from long division: the numerator divided by the denominator. The calculator first puts the fraction in lowest terms, so 6/8 is treated as 3/4, then divides exactly, digit by digit, with no rounding along the way. Whether the decimal stops depends only on the denominator in lowest terms. If its only prime factors are 2 and 5, the division ends, and the number of digits after the point is the larger of the two exponents: 8 is 2 x 2 x 2, so 3/8 ends after 3 digits. Any other prime factor makes the digits cycle forever, because long division can only leave so many different remainders before one comes back. The repeating block is shown in parentheses, which stands in for the bar written over repeating digits in a textbook: 1/7 is 0.(142857), a 6-digit cycle. Mixed numbers work too, so 2 1/3 becomes 2.(3). The rounded figure is worked out from the exact fraction, not from a shortened decimal, so it is right to the last place you ask for.
Frequently asked questions
How do I convert a fraction to a decimal by hand?+
Divide the numerator by the denominator with long division. For 3/8, 8 goes into 3.000 to give 0.375. If a remainder you have already seen comes back, the digits from that point repeat.
Why do some fractions give repeating decimals?+
A decimal ends only when the denominator, in lowest terms, is built from 2s and 5s, the prime factors of 10. Thirds, sixths, sevenths and ninths have other factors, so their digits cycle: 1/6 becomes 0.1(6) and 1/7 is 0.(142857).
What do the parentheses mean?+
They mark the digits that repeat forever, the same job a bar over the digits does on paper. 0.1(6) means 0.16666 and so on. Very long cycles are cut after 60 digits, and the page says when that happens.
How do I write a fraction as a percent?+
Multiply its decimal by 100. 3/8 is 0.375, which is 37.5%, and 2/3 becomes 66.(6)%, about 66.67% when rounded.
How do I turn a decimal back into a fraction?+
That runs the other way, so it has its own page: the Decimal to Fraction Calculator, linked under More Math tools below. It reads 0.375 as 3/8 and a repeating 0.(6) as 2/3.
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