Decimal to Fraction Calculator
Change a terminating or repeating decimal into a fraction in lowest terms.
How to use the Decimal to Fraction Calculator
- Enter the decimal number – For 0.1666… enter 0.1 here and 6 as the repeating digits.
- Enter the repeating digits (optional).
- Press Calculate. The result updates automatically as you type.
About the Decimal to Fraction Calculator
Fractions are often easier to read and measure with than decimals: a woodworker wants 5/8″, not 0.625″, and a recipe calls for 1/3 cup, not 0.333 cup. Converting by hand is mechanical, and this tool does it exactly rather than by rounding, so 0.1 becomes precisely 1/10.
For a repeating decimal, enter the part before the repeat in the first box and the repeating digits in the second. For 0.454545…, enter 0 and 45 to get 5/11; for 2.8333…, enter 2.8 and 3 to get 17/6. If you only need the nearest ruler fraction (sixteenths), round the result accordingly.
Formula
Terminating: 0.625 = 625 / 1000 = 5/8
Write the digits after the decimal point over a power of ten (10, 100, 1000…) with as many zeros as there are decimal places, then divide both parts by their greatest common factor.
Repeating: 0.1666… = (1 × 9 + 6) / (10 × 9) = 15/90 = 1/6
A repeating block of m digits is divided by 10m − 1 (9, 99, 999…), shifted past any non-repeating digits.
Example calculation
Using the default values:
- Decimal number = 0.625
the calculator returns:
- Fraction: 5/8
- Mixed number: 5/8
Frequently asked questions
How do I convert 0.75 to a fraction?
0.75 has two decimal places, so write 75/100, then divide both by 25 to get 3/4.
How do I convert a repeating decimal to a fraction?
Put the repeating block over as many 9s as it has digits. 0.272727… = 27/99 = 3/11.
Is 0.999… equal to 1?
Yes. Using the rule, 0.999… = 9/9 = 1. Both expressions name the same number.
Last updated: · Category: Math calculators