Decimal to Fraction Calculator
Turn any decimal into its simplest exact fraction and mixed number.
What the Decimal to Fraction Calculator does
This uses a continued-fraction expansion, which finds the simplest fraction matching your decimal rather than just putting it over a power of ten. That is why 0.333333 comes back as 1/3 instead of 333333/1000000.
Formula
Expand the decimal as a continued fraction, then reduce by the GCD
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Decimal value | number | Yes | — |
How to use it
- Enter Decimal value.
- Select Calculate.
Worked example
Convert 0.625 into a fraction.
- Decimal value
- 0.625
0.625 = 625/1000, which reduces to 5/8.
Reading the result
- The answer is the simplest fraction matching the decimal to the precision you gave, which is not always the fraction the decimal originally came from.
Assumptions and limitations
- The decimal you type is treated as the exact value. 0.333333 is read as an approximation of 1/3, which is usually the intent but not always.
Common mistakes
- Expecting an exact fraction for an irrational number. π and √2 have no fractional form, so any result is an approximation.
- Treating the fraction as exact after entering a rounded decimal — it can only be as accurate as what you typed.
Frequently asked questions
Can every decimal become a fraction?
Every terminating or repeating decimal can. Irrational numbers like π cannot, so you only ever get a close approximation.