Convert any decimal into a fraction in lowest terms, including repeating decimals.
How the decimal to fraction calculator works
Terminating decimals convert exactly: 0.375 is 375/1000, which reduces to 3/8. The calculator finds the best rational form using continued fractions, which produces the simplest fraction rather than an unwieldy one.
Repeating decimals need the classic algebra trick, and the calculator applies it when you tell it how many digits repeat — 0.333… with one repeating digit becomes exactly 1/3.
Step by step
- Enter your decimal value.
- If it repeats, say how many digits at the end repeat.
- Read the fraction in lowest terms.
The calculation
terminating: write over a power of ten and reduce
repeating: (full − non-repeating part) ÷ (9…9 0…0)
The default scenario, worked through
As an example, with a decimal value of 0.375, the calculator returns a as a fraction of 3/8. Underneath, Simplified fraction comes out at 3/8 and Mixed number at 3/8. Change any field and every figure updates as you type.
Common questions
How do I convert a repeating decimal?
Set the repeating digit count. For 0.1666… with one repeating digit, the calculator returns 1/6 exactly.
Why is the max denominator setting there?
It caps how complicated the fraction is allowed to get. Lower it for a simpler approximation, raise it for more precision.
Is every decimal a fraction?
Every terminating or repeating decimal is. Irrational numbers like π never terminate or repeat, so only approximations are possible.