Decimal to fraction calculator
Turn a terminating or recurring decimal into an exact fraction in lowest terms.
Fraction
Fraction: 3/8
- Mixed number
- 3/8
- Decimal value
- 0.375
Step by step
- 0.375 = 375/1000
- = 3/8
How it works
A terminating decimal is a whole number over a power of ten: 0.375 is 375/1000. Dividing top and bottom by their greatest common divisor gives the simplest form, 3/8.
For a recurring decimal, take all the digits up to the end of the first repeat and subtract the digits before the repeat. Divide by as many 9s as there are repeating digits, followed by as many 0s as there are non-repeating decimals.
The result is always exact: every recurring decimal is a fraction.
Formula
0.abc = abc / 1000 0.a(b) = (ab − a) / 90 0.(ab) = ab / 99
Worked example
0.375 = 375/1000 = 3/8. For 0.1666…, written 0.1(6): (16 − 1) ÷ 90 = 15/90 = 1/6.
Questions people ask
Is 0.999… really equal to 1?
Yes. Using the rule, 0.(9) = 9/9 = 1. The two are different ways of writing the same number.
How do I type a recurring decimal?
Put the repeating block in brackets: 0.(142857) for 1/7, or 2.4(5) for 2.4555…
Why can’t I convert π to a fraction?
π is irrational: its decimals never end or repeat, so no fraction equals it exactly. 22/7 and 355/113 are only approximations.