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Decimal to Fraction Calculator

Convert any decimal, including repeating decimals like 0.333… or 0.1666…, to a fraction in simplest form, with the mixed number and the steps.

Results

ItemValue

Steps

StepWorking
Exact for any decimal you can type. For a repeating decimal, put the repeating part in brackets: 0.(3) is 0.333…, 0.1(6) is 0.1666…, and 0.(142857) is 1/7.

Quick Answer

To turn a decimal into a fraction, write it over a power of 10 and simplify. 0.625 = 625/1000, and dividing both by their GCD of 125 gives 5/8. For a repeating decimal like 0.333…, x = 0.(3) gives 10x − x = 3, so x = 3/9 = 1/3.

Last updated: 3 November 2026 ·How we calculate this: place value and the greatest common divisor

Table of Contents

How This Decimal to Fraction Calculator Works

Type a decimal such as 0.625, 2.75 or −1.2. For a repeating decimal, put the repeating digits in brackets, so 0.333… is 0.(3) and 0.1666… is 0.1(6). The calculator writes the decimal as a fraction, finds the greatest common divisor (GCD) to simplify it, and shows the mixed number, the decimal and the percent.

Quick explanation: each decimal place is a power of 10.

  • One place: tenths, so 0.7 = 7/10.
  • Two places: hundredths, so 0.25 = 25/100 = 1/4.
  • Repeating: use the subtraction trick to remove the endless part.

How to Use the Decimal to Fraction Calculator

  1. Type the decimal number.
  2. For repeating digits, put them in brackets, such as 0.(6).
  3. Press Calculate.
  4. Read the simplest fraction and mixed number.
  5. Check the steps to see how it was simplified.

Core Methods

  • Terminating decimal: write the digits over 10k, where k is the number of decimal places, then simplify
  • Simplify: divide the top and bottom by their GCD
  • Pure repeating: 0.(R) = R ÷ (10r − 1), such as 0.(27) = 27/99 = 3/11
  • Mixed repeating: subtract the non-repeating part, as in the steps
  • Mixed number: whole part = top ÷ bottom, remainder over the bottom

Key Terms

  • Numerator: the top number of a fraction.
  • Denominator: the bottom number of a fraction.
  • Simplest form: a fraction whose top and bottom share no common factor except 1.
  • GCD: greatest common divisor, the largest number that divides both.
  • Repeating decimal: a decimal with digits that repeat forever in a pattern.

Worked Example

Convert 0.1666… to a fraction.

  • Let x = 0.1(6). Then 100x = 16.666… and 10x = 1.666…
  • 100x − 10x = 15, so 90x = 15
  • x = 15/90 = 1/6

Real-Life Examples

  • Woodworking: 0.4375 inches is 7/16 of an inch.
  • Cooking: 0.75 cup is 3/4 cup, and 0.333… cup is 1/3 cup.
  • Homework: 2.125 = 17/8 = 2 1/8.
  • Odds and ratios: 0.2 is 1/5, or 1 in 5.

Terminating vs Repeating Decimals

  • Terminating: ends, like 0.375. Its simplest denominator has only 2s and 5s as prime factors.
  • Repeating: goes on in a pattern, like 0.142857142857… = 1/7.
  • Irrational: never repeats, like π, and cannot be written exactly as a fraction.

Common Decimals as Fractions

DecimalFractionDecimalFraction
0.11/100.51/2
0.1251/80.63/5
0.21/50.6255/8
0.251/40.753/4
0.33/100.84/5
0.3753/80.8757/8
0.42/50.99/10
0.333…1/30.666…2/3

Tips

  • Inch measurements: results like 3/8 or 5/16 have denominators that are powers of 2.
  • Rounded decimals: 0.33 is 33/100, not 1/3. Use 0.(3) for one third.
  • Negative numbers: the minus sign stays in front of the fraction.
  • Whole numbers: 4 is 4/1.

Rounding a Decimal to the Nearest Fraction

Sometimes you need a handy fraction, not the exact one. A tape measure shows sixteenths of an inch, and a recipe uses halves, thirds and quarters. To round a decimal to the nearest fraction with a chosen denominator, multiply the decimal by that denominator, round to a whole number, and put it back over the denominator.

  • Nearest 1/16: 0.53 × 16 = 8.48, which rounds to 8, so 8/16 = 1/2.
  • Nearest 1/8: 0.69 × 8 = 5.52, which rounds to 6, so 6/8 = 3/4.
  • Nearest 1/4: 2.2 × 4 = 8.8, which rounds to 9, so 9/4 = 2 1/4.

Rounding gives an easy fraction close to the decimal, while this calculator gives the exact fraction. For example, 0.53 exactly is 53/100, but to the nearest sixteenth it is 1/2. Use the exact answer for math and the rounded one for measuring.

Common Mistakes to Avoid

  • Not simplifying. 50/100 should be 1/2.
  • Treating a rounded decimal as repeating. 0.67 is 67/100, not 2/3.
  • Counting places wrong. 0.05 is 5/100, not 5/10.
  • Losing the whole number. 3.5 is 7/2, or 3 1/2.
  • Dropping the minus sign. −0.25 is −1/4.

Frequently Asked Questions

Write the digits over 10, 100 or 1,000, depending on the decimal places, then simplify.

5/8.

1/3. Enter it as 0.(3).

3/4.

Put the repeating digits in brackets: 0.(6) for 0.666…, or 2.4(18) for 2.41818…

1/6.

Divide the top by the bottom. The quotient is the whole number and the remainder goes over the bottom.

Every terminating or repeating decimal can. Irrational numbers like π cannot.

1/5.

3/2, or 1 1/2.

With x = 0.(9), 10x − x = 9, so x = 1. Try 0.(9) in the calculator.

Divide the top by the bottom, or use our Fraction Calculator.

References & Sources

SourceUsed ForLink
Wikipedia, Repeating decimal Why repeating decimals are fractions, and how to convert them. https://en.wikipedia.org/wiki/Repeating_decimal
Wikipedia, Greatest common divisor How the GCD is used to simplify fractions. https://en.wikipedia.org/wiki/Greatest_common_divisor