Tools

Decimal to Fraction Converter

Turn decimals, including repeating ones, into fractions

Use a/b for fractions, 2 1/3 for mixed numbers, and + − × ÷ ^ ( ).

Simplified fraction
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Mixed number
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Decimal
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For repeating decimals, put the repeating part in brackets: 0.(3) = 0.333…, 0.1(6) = 0.1666…

Fraction
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Mixed number
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How to convert a decimal to a fraction

  1. Type the decimal in the first box, such as 0.375 or 2.125.
  2. For a repeating decimal, put the repeating part in brackets: 0.(3) for 0.333…, 0.(142857) for 1/7, or 0.1(6) for 0.1666…
  3. Read the simplified fraction and the mixed number, with the steps used.

The method

For a terminating decimal, write the digits over the matching power of ten and simplify: 0.375 = 375/1000. The greatest common factor of 375 and 1000 is 125, so the fraction is 3/8. 2.125 = 2125/1000 = 17/8 = 2 1/8.

For a repeating decimal, subtract to cancel the repeating part. For 0.1666…: let x = 0.1666…; then 10x = 1.666… and 100x = 16.666…, so 90x = 15 and x = 15/90 = 1/6. The rule of thumb: the repeating digits go over as many 9s as they have digits, followed by a 0 for each non-repeating digit after the point.

DecimalFraction
0.51/2
0.251/4
0.753/4
0.21/5
0.1251/8
0.333…1/3
0.666…2/3
0.1666…1/6
0.06251/16
0.142857…1/7

FAQ

What is 0.75 as a fraction?

3/4.

How do I convert 0.333 to a fraction?

If it means 0.333… repeating, it is 1/3 (type 0.(3)). Exactly 0.333 is 333/1000.

Can every decimal be written as a fraction?

Every terminating or repeating decimal can. Decimals that never repeat, such as π, are irrational and cannot.