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Decimal to Fraction Calculator

Type a decimal to get it as a fraction in lowest terms and as a mixed number. It also understands repeating decimals — write 0.1(6) for 0.1666… — and suggests the closest simple fraction when your decimal has been rounded, such as 0.3333.

Quick examples

For a repeating decimal put the repeating digits in parentheses, e.g. 0.1(6), or end with … to get the closest simple fraction.

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Fraction3/8
As a mixed number
3/8
Closest simple fraction
3/8
Closest simple fraction as a decimal
0.375

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      Formula

      Terminating decimal: write the digits over a power of ten, then reduce. 0.375 = 375/1000 = 3/8
      Repeating decimal: (all digits up to the end of the first repeating block − the non-repeating digits) ÷ (one 9 per repeating digit, followed by one 0 per non-repeating decimal digit). 0.1(6) = (16 − 1)/90 = 15/90 = 1/6
      Closest simple fraction: the best continued-fraction approximation whose denominator does not exceed your limit

      How to use it

      1. Type the decimal exactly as you have it.
      2. If digits repeat forever, put the repeating part in parentheses — 0.(3), 0.1(6), 0.(142857) — or end the number with … to ask for the closest simple fraction.
      3. Read the exact fraction and the mixed number.
      4. If your decimal was rounded, look at the closest simple fraction and adjust the largest denominator allowed if needed.

      Worked examples

      0.375 as a fraction

      Fraction
      3/8
      Closest simple fraction
      3/8

      2.75 as a fraction

      Fraction
      11/4
      As a mixed number
      2 3/4

      The repeating decimal 0.1(6), that is 0.1666…

      Fraction
      1/6

      0.3333 typed as a rounded value

      Fraction
      3333/10000
      Closest simple fraction
      1/3

      Rounded decimals

      A calculator display such as 0.3333 is not exactly one third; taken literally it is 3333/10000. The “closest simple fraction” line finds the nearest fraction with a small denominator — 1/3 in this case — using continued fractions.

      The denominator limit controls how simple “simple” is. For 3.14159265 a limit of 10 gives 22/7, a limit of 100 gives 311/99 and a limit of 1,000 gives 355/113.

      Why every repeating decimal is a fraction

      Take x = 0.1666… Then 100x = 16.666… and 10x = 1.666…, so subtracting gives 90x = 15 and x = 15/90 = 1/6. The same trick works for any repeating pattern, which is why decimals that neither end nor repeat (like π or √2) cannot be written as fractions.

      Questions people ask

      What is 0.375 as a fraction?

      3/8. Write it as 375/1000 and divide the top and bottom by 125.

      What is 0.75 as a fraction?

      3/4. It is 75/100, and dividing both by 25 gives 3/4.

      What is 0.333 repeating as a fraction?

      1/3. Enter it as 0.(3). If you enter 0.333 without marking the repeat, the exact answer is 333/1000 and the closest simple fraction is 1/3.

      What is 2.75 as a fraction?

      11/4, or 2 3/4 as a mixed number.

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