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Decimal to Fraction Calculator

Enter a decimal such as 0.625 or a repeating decimal such as 0.1(6). You get the simplified fraction, the mixed number and the steps, or the closest simple fraction with a denominator limit.

Put repeating digits in brackets: 0.(3) = 0.333…, 0.1(6) = 0.1666…, 2.(142857)

Conversion

e.g. 16 for inch fractions, 1000 for close fits

Enter your values to see the result.
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How to use the Decimal to Fraction Calculator

  1. Type the decimal. Put repeating digits in brackets, e.g. 0.(6).
  2. Choose Exact for the precise fraction, or Simplest approximation to round to a simple fraction.
  3. Set the largest denominator (approximation mode), e.g. 16 for inches.
  4. Press Convert; results also update as you type.
  5. Read the fraction, mixed number and the step-by-step working.

Decimal to fraction formulas

Terminating decimal: with k decimal places, x = (digits without the point) / 10k, then divide top and bottom by their greatest common divisor. Example: 2.375 = 2375/1000 = 19/8.

Repeating decimal: for x = I.N(R), where N has n digits and the repeating block R has r digits:
x = (INR − IN) / (99…9 00…0), with r nines and n zeros. Example: 1.2(45) = (1245 − 12) / 990 = 1233/990 = 137/110.

Common decimals as fractions

DecimalFractionDecimalFraction
0.11/100.06251/16
0.1251/80.18753/16
0.21/50.31255/16
0.251/40.(3)1/3
0.3753/80.(6)2/3
0.51/20.1(6)1/6
0.6255/80.8(3)5/6
0.753/40.(142857)1/7
0.8757/80.(09)1/11

Need the reverse? The fraction to decimal calculator shows the repeating digits of any fraction.

Frequently asked questions

How do you convert a decimal to a fraction?

Write the decimal over a power of ten with as many zeros as decimal places, then simplify. 0.625 = 625/1000; the greatest common divisor is 125, so it simplifies to 5/8.

How do you convert a repeating decimal to a fraction?

For 0.(3): let x = 0.333…, then 10x = 3.333…, and 10x − x = 3, so x = 3/9 = 1/3. In general, subtract the number without the repeating block from the number including one block, and divide by as many 9s as repeating digits followed by as many 0s as non-repeating decimal digits.

What is 0.333 as a fraction?

Exactly, 0.333 = 333/1000. If you mean the repeating decimal 0.333…, enter 0.(3) to get 1/3, or use Simplest approximation, which also returns 1/3.

What is 0.1666… as a fraction?

Enter 0.1(6). x = (16 − 1) / 90 = 15/90 = 1/6.

What does the simplest approximation mode do?

It finds the fraction closest to your decimal whose denominator does not exceed the limit you set, using continued fractions. For example 3.14159 with a limit of 1000 gives 355/113.

How do I write a decimal as a mixed number?

Convert to an improper fraction, then divide: 2.375 = 2375/1000 = 19/8, and 19 ÷ 8 = 2 remainder 3, so it is 2 3/8.

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