Decimal to Fraction Calculator
Free decimal to fraction calculator: turn any decimal, including repeating decimals like 0.333…, into a simplified fraction and a mixed number.
Put the repeating part in parentheses: 0.(3) is 0.333… and 0.1(6) is 0.1666…
Step by step
What it does
Every decimal that ends, or that repeats forever, is a fraction. A decimal that ends is the digits over a power of ten: 0.75 = 75/100, which simplifies to 3/4. For a repeating decimal, type the part that repeats in parentheses: 0.(3) means 0.333… and equals 1/3, and 0.1(6) means 0.1666… and equals 1/6. The conversion is exact.
How to use it
- Type the decimal, for example 0.625 or 2.5.
- If the decimal repeats, put the repeating digits in parentheses.
- Read the simplified fraction and the mixed number.
The arithmetic runs in your browser. Nothing you type is sent anywhere and nothing is stored, so you can use these with real numbers.
Frequently asked questions
How do I convert 0.625 to a fraction?
There are three decimal places, so write it over 1,000: 625/1000. The greatest common divisor is 125, so it simplifies to 5/8.
What fraction is 0.333…?
Exactly 1/3. Rounded values such as 0.33 or 0.333 are different fractions (33/100, 333/1000); to get 1/3, type 0.(3).
Which fractions have a decimal that ends?
Those whose simplified denominator has no prime factors other than 2 and 5, such as 1/8 = 0.125 or 3/20 = 0.15. Any other denominator, such as 3, 7 or 12, gives a repeating decimal.
What about numbers like π or √2?
They are irrational: their decimals never end and never repeat, so no fraction is exactly equal to them. You can still convert a rounded value, such as 3.14 = 157/50.
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Wikipedia — Fraction
Wikipedia — Greatest common divisor
Wikipedia — Repeating decimal