Decimal to Fraction Calculator

A decimal to fraction calculator turns a decimal into an exact fraction in its simplest form. Terminating decimals are written over a power of ten and simplified. Repeating decimals, such as 0.333… or 0.1666…, are converted with the standard algebra method, where the repeating part cancels out by subtraction.

Put repeating digits in brackets: 0.(3) means 0.333…
Try:

How to use the decimal to fraction calculator

  1. Type the decimal, such as 0.375.
  2. For repeating digits, put them in brackets: 0.(3) means 0.333….
  3. Press Calculate to see the fraction and the method.

Formula

0.a‾=a9,0.ab‾=ab990.\overline{a} = \frac{a}{9}, \quad 0.\overline{ab} = \frac{ab}{99}

Worked example: 0.375

  • Decimal: 0.375

✓ Answer checked

38\frac{3}{8}
Step-by-step working (2 steps)

  1. Count decimal places Place value

    There are 3 decimal places, so write the number over 1000.

    0.375=37510000.375 = \frac{375}{1000}

  2. Simplify

    Divide the top and bottom by their greatest common factor.

    =38= \frac{3}{8}
Formulas used
0.a‾=a9,0.ab‾=ab990.\overline{a} = \frac{a}{9}, \quad 0.\overline{ab} = \frac{ab}{99}
How this was checked
  • ✓ Dividing 3/8 gives 0.375…, matching the decimal.

Frequently asked questions

How do I convert a decimal to a fraction?

Write the digits after the point over 10, 100 or 1000 depending on the number of decimal places, then simplify. 0.375 = 375/1000 = 3/8.

How do I convert a repeating decimal to a fraction?

Call it x, multiply by a power of 10 so the repeats line up, and subtract. For 0.333…, 10x − x = 3, so x = 1/3.

How do I type a repeating decimal?

Put the repeating digits in brackets. For example, 0.1(6) means 0.1666….

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