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Decimal to Fraction Converter

Exact fractions from decimals — repeating decimals too — with the working shown.

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Repeating decimals: put the repeating part in brackets, 0.(3) or 2.1(6), or type it three times with dots, 0.1666...

Fraction
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Quick Tool Overview

Decimal to Fraction converts terminating and repeating decimals into exact fractions in lowest terms with the working shown, and can round to the nearest eighth or sixteenth or the closest small-denominator fraction.

What it does
Converts decimals to simplified fractions
You give it
A decimal, including repeating ones like 0.(3)
You get back
The fraction, mixed number, percentage and steps
Best for
Maths homework, recipes and measurements
Converters Free, unlimited use No sign-up Runs in your browser

About the Decimal to Fraction Converter

Every terminating decimal is a fraction over a power of ten, and every repeating decimal is a fraction too — you just have to reduce it. The method is taught in school and forgotten by the time you need to cut a board to 0.3125 inches or check that 0.1666… really is one sixth.

Type a decimal and the converter gives the exact fraction in lowest terms with the working: the power of ten, the greatest common divisor, and the result. Repeating decimals are written with the repeating part in brackets, 0.(3), or typed three times with dots. Two further modes find the closest fraction with a small denominator, or round to the nearest eighth or sixteenth for a tape measure, and say how far off each is.

Key features of the Decimal to Fraction Converter

Repeating decimals

0.(3), 1.2(142857) and 0.1666... are converted to their exact fractions.

Working shown

The power of ten, the greatest common divisor and the reduced result are written out.

Ruler rounding

Round to the nearest quarter, eighth, sixteenth, thirty-second or sixty-fourth.

Closest simple fraction

Find the best fraction under a denominator limit, with the error it introduces.

Every related form

Mixed number, decimal, percentage and ratio are shown with the fraction.

How to use the Decimal to Fraction Converter

  1. 1

    Type the decimal

    Such as 0.625, -2.75 or 0.(142857) for a repeating decimal.

  2. 2

    Choose the mode

    Exact gives the true fraction; closest limits the denominator; rounding snaps to quarters, eighths or sixteenths.

  3. 3

    Read the fraction

    The simplest form, the mixed number and the percentage are shown together.

  4. 4

    Follow the working

    The steps show how the fraction was reached, which is what homework needs.

Frequently asked questions

Write it over a power of ten — 0.625 is 625/1000 — then divide top and bottom by their greatest common divisor, 125, to get 5/8.

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