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Decimal to Fraction Converter: Exact and Simple Fractions

This free converter turns a decimal number into a fraction. It gives the exact fraction, the mixed number and a list of the best simple approximations, which is handy for repeating decimals such as 0.333333.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

Decimals and fractions are two ways of writing the same number. Recipes, measurements and maths often need the fraction. Finite decimals convert exactly, and repeating ones need a close fraction.

Type a decimal and read the fractions.

How to Use This Tool

  1. Enter the value or values asked for in the boxes.
  2. Choose the unit label if there is a choice.
  3. Press Calculate.
  4. Read every result in the table and copy what you need.

How the Calculation Works

The exact fraction uses the digits after the decimal point as the numerator and 10 to that many places as the denominator, divided by the greatest common divisor. For approximations the tool expands the number as a continued fraction and lists each convergent until the denominator reaches your limit.

Worked Example

0.75 is exactly 3/4. 0.125 is 1/8. 3.14159 is exactly 314159/100000, with the best simple approximations 22/7, 333/106 and 355/113.

Common Uses

  • Recipes and measurements.
  • Maths homework.
  • Woodwork and sewing.
  • Understanding repeating decimals.

Tips and Common Mistakes

  • Enter a decimal with a point, not a comma.
  • Large decimals give large exact fractions.
  • Use the approximation list for a practical value.
  • Measure carefully: a small error in a length is squared in an area and cubed in a volume, so a 5 percent error in a side can become a 10 percent error in the area or a 15 percent error in the volume.
  • Round only at the end. If you copy a result into another calculation, copy the full number from the tool rather than a rounded one, so small errors do not build up.

Next, you may need the fraction to decimal converter, simplify radical calculator, system of equations solver, circle calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

Write the digits over a power of ten, then simplify. 0.75 is 75/100, which simplifies to 3/4.
A decimal like 0.333333 is only an approximation of 1/3. The approximation list finds 1/3 as the simplest fraction that is very close.
With continued fractions, which give the best rational approximations for a given size of denominator.
Because 22/7 is the best approximation of 3.14159 with a denominator under 100. 355/113 is better, with a denominator under 1,000.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.