Decimal to Fraction Calculator
Convert a decimal to a fraction in its simplest form. Type any decimal, including repeating decimals with the repeating part in parentheses, to see the fraction, the mixed number, and the percentage.
Fraction
3/8
Check the highlighted fields to see your result.
- Mixed number
- Not needed
- Percentage
- 37.5%
Results are estimates for information only and do not constitute financial, medical, or legal advice.
How it works
Write the decimal as a fraction over a power of 10: one decimal place goes over 10, two over 100, three over 1,000, and so on. Then simplify by dividing the top and bottom by their greatest common factor.
The formulas
0.375 = 375 ÷ 1,000 = 3/8
Repeating: 0.1(6) = (16 − 1) ÷ 90 = 1/6
For a repeating decimal, subtract the digits before the repeat from all the digits, and divide by as many 9s as repeating digits, followed by as many 0s as non-repeating decimal digits.
Worked example
Convert 0.375 to a fraction.
- Three decimal places, so 0.375 = 375/1,000.
- The greatest common factor of 375 and 1,000 is 125.
- 375 ÷ 125 = 3 and 1,000 ÷ 125 = 8, so 0.375 = 3/8.
Frequently asked questions
How do I convert a repeating decimal?
Put the repeating part in parentheses. For 0.333…, type 0.(3) and you get 1/3. For 0.1666…, only the 6 repeats, so type 0.1(6) and you get 1/6. If you type 0.333 without parentheses, the calculator treats it as exactly 333/1000.
What is a mixed number?
A whole number plus a proper fraction, like 2 3/4. It means the same as the improper fraction 11/4, and it is often easier to read in recipes and measurements.
Why is 0.(9) equal to 1?
Because 0.999… with nines forever is exactly 1, not just close to it. One way to see it: 1/3 = 0.333…, and 3 × 0.333… = 0.999…, while 3 × 1/3 = 1.