Decimal to Fraction Calculator

Exact fractions, recovered by continued fractions.

Written and maintained by Mohit PatelLast checked August 4, 2026How we build these

Decimal

Largest denominator

Lower this to find a simpler near-equivalent.

As a fraction

3/4

Fraction3/4

Mixed number3/4

As a decimal0.75

As a percentage75.0000%

ExactYes

Decimal terminatesYes

This uses the continued fraction expansion rather than the schoolbook method of multiplying by a power of ten. The difference matters for recurring decimals: 0.333333 becomes 1/3 rather than 333333/1000000, and 3.142857 recovers 22/7. A fraction's decimal terminates exactly when its reduced denominator has no prime factors besides 2 and 5 — the primes that divide ten.

How the Decimal to Fraction Calculator works

This uses the continued fraction expansion rather than multiplying by a power of ten, and the difference matters for recurring decimals: 0.333333 becomes 1/3 rather than 333333/1000000, and 3.142857 recovers 22/7.

Also known as: convert decimal to fraction · decimal as a fraction · repeating decimal to fraction · fraction converter

Why not just use a power of ten

The schoolbook method puts the digits over a power of ten and reduces: 0.75 becomes 75/100, then 3/4. That works perfectly for decimals that terminate.

It fails on recurring ones. 0.333333 becomes 333333/1000000, which is close to a third but is not it, and no amount of reducing will get there.

Continued fractions

This page uses the continued fraction expansion instead, which finds the simplest fraction within a tolerance rather than the most literal one.

It recovers 1/3 from 0.333333 and 1/7 from 0.142857. Lowering the maximum denominator finds deliberately simpler approximations — which is how 3.14159 yields 22/7, the classic approximation of π.

A fraction's decimal terminates exactly when its reduced denominator has no prime factors besides 2 and 5, the primes that divide ten. Halves, quarters, fifths and eighths terminate; thirds, sevenths and ninths do not.

Where to go next

The Decimal to Fraction question rarely arrives on its own. These are the ones that usually come with it:

Fraction to Decimal Calculator — Decimal, percentage, and whether it terminates.
Mixed Number Calculator — Mixed numbers to improper fractions and back.
Ratio Calculator — Simplify a ratio, and see it as shares of the whole.
Percentage Calculator — Every common percentage question in one place.

Sources

NIST Digital Library of Mathematical Functions

Frequently asked questions

How do I convert a decimal to a fraction?

The schoolbook method puts the digits over a power of ten and reduces. That fails on recurring decimals, so this uses continued fractions, which recover 1/3 from 0.333333.

Why does 0.333333 become 1/3 and not 333333/1000000?

Because the continued fraction expansion finds the simplest fraction within a tolerance, and 1/3 is far simpler while being closer to the intended value.

Which decimals terminate?

Those whose reduced denominator has no prime factors besides 2 and 5 — the primes that divide ten. A third recurs; a quarter does not.

What is the largest denominator setting for?

Capping how complex the fraction may get. Lowering it finds a simpler near-equivalent, which is how 3.14159 yields 22/7.

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The one-line version

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