Decimal to Fraction Converter

Convert any decimal number to a simplified fraction, mixed number, and closest simple fraction.

Decimal to Fraction Converter tool

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Example

Input: Decimal 0.625

Result: 5/8 (unsimplified 625/1000, 62.5 %)

0.625 has 3 decimal places, so it equals 625/1000; dividing both parts by their GCD of 125 gives 5/8.

Decimals to Fractions at a Glance

DecimalExact fractionClosest simple fraction
0.1251/8Same
0.21/5Same
0.251/4Same
0.3753/8Same
0.63/5Same
0.6255/8Same
0.8757/8Same
1.757/4Same
0.33333333/100001/3 (approx.)
0.66676667/100002/3 (approx.)
0.16671667/100001/6 (approx.)
0.14291429/100001/7 (approx.)
0.0833833/100001/12 (approx.)

Rounded decimals such as 0.3333 give an exact fraction over 10,000 and a close simple match.

  1. Enter a decimal number in the input field.
  2. For repeating decimals, enter several repeating digits (such as 0.3333) and check the Closest Simple Fraction result.
  3. View the exact fractional representation simplified to lowest terms.
  4. Compare the unsimplified fraction with the reduced result, and review the mixed number and percentage.
  5. Click the copy button to copy the fraction result.

Turning Decimals Into Exact Fractions

To convert a decimal to a fraction, write it over a power of 10 and simplify: 0.75 = 75/100 = 3/4. This converter does that for any decimal you type. It shows the fraction in lowest terms, the unsimplified version, a mixed number for values above 1, and the percent.

The number of decimal places sets the starting fraction. One place goes over 10, two places over 100, three over 1,000. So 0.625 starts as 625/1000. Both parts are then divided by their greatest common divisor, which is 125 here, to give 5/8. The tool keeps every digit you type, so the fraction is exact for what you entered.

That exactness matters for rounded repeating decimals. If you type 0.3333, the exact fraction is 3333/10000, not 1/3, because 0.3333 is a little less than a third. To help, the converter also shows the Closest Simple Fraction. This is the best fraction with a bottom number of 1,000 or less that lands within 0.1% of your decimal. For 0.3333 it is 1/3 (approx.). It is also handy for calculator results: 3.14159 gives 355/113, a well-known close match for pi.

You will use this most for measurements and recipes. A drawing that says 0.375 inches means 3/8 inch, and 0.75 cup is 3/4 cup. A decimal above 1, such as 1.75, gives 7/4 and the mixed number 1 and 3/4. For the reverse direction, try the Fraction to Decimal Converter. To do math with the result, use the Fraction Calculator.

Formula / How It Works

For terminating decimal with n decimal places: Fraction = Decimal x 10^n / 10^n, then simplify by GCD

Frequently Asked Questions

Count the decimal places, write the digits over 1 followed by that many zeros, then simplify. For 0.75, that is 75/100. Both numbers divide by 25, which gives 3/4. For 0.125 it is 125/1000, and dividing by 125 gives 1/8.
Use a little algebra. Let x = 0.333... Then 10x = 3.333... Subtract the first line from the second to get 9x = 3, so x = 1/3. In this converter, type several repeating digits, such as 0.3333, and read the Closest Simple Fraction result, which shows 1/3 (approx.).
It is the fraction with a denominator of 1,000 or less that is nearest to your decimal. It only appears when it is within 0.1% of your value and differs from the exact fraction. It marks itself as approximate when it does not match exactly. It is useful for rounded values such as 0.6667, which gives 2/3.
Every decimal that ends or repeats can be written exactly as a fraction of whole numbers. Numbers such as pi and the square root of 2 go on forever without repeating, so no fraction equals them exactly. You can still find close fractions, such as 22/7 or 355/113 for pi.

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