Decimal to Fraction Converter

This decimal to fraction converter turns any terminating decimal into a simplified fraction. Converting a decimal to a fraction is a two-step process: express the decimal over a power of ten, then reduce. This calculator does both and shows the working, so 0.75 becomes 75/100 and then 3/4, with the mixed number and percentage alongside.

The method

0.75  → 75/100  → divide by GCD 25 → 3/4
1.625 → 1625/1000 → divide by GCD 125 → 13/8 → 1 5/8

The number of decimal places sets the denominator: one place is /10, two is /100, three is /1000.

Exact by design

Because the conversion reads the typed digits rather than a binary float, common decimals land on clean fractions instead of artifacts like 3377699720527855/4503599627370496. Repeating decimals are the one caveat — they are converted as the finite value you enter.

Worked example

Converting 0.625:

three decimal places → denominator 1,000
0.625          → 625/1000
GCD(625, 1000) → 125
reduced        → 5/8

The denominator is set entirely by how many decimal places you type, and the reduction afterwards is exact. Enter 1.625 and the same path gives 1625/1000, reduced by 125 to 13/8, shown as the mixed number 1 5/8 and as 162.5%.

Repeating decimals do not become what you expect

Enter 0.333 and the answer is 333/1000, already in its lowest terms, and it is not 1/3. That is correct behaviour rather than a failure: one third is 0.3333... with the 3 repeating forever, and any finite string of digits is a slightly different number. The tool converts the digits you actually typed.

The distinction stays invisible until it matters. A genuine repeating decimal converts by an algebraic step rather than a power of ten — for 0.333... you set x = 0.333..., multiply by ten to get 10x = 3.333..., subtract to get 9x = 3, and conclude x = 1/3. This page does not perform that step because it cannot know whether you meant three decimal places or an endless one. If you want the exact third, type it as a fraction in Fraction Calculator and work with 1/3 directly.

Why it reads your digits instead of a floating-point number

Binary floating point cannot represent most decimal fractions exactly. A naive conversion that routes through a 64-bit double can return 3377699720527855/4503599627370496 for a value you typed as 0.75, which is technically the closest representable binary number and completely useless to anybody holding a tape measure.

This implementation parses the typed characters instead, so the decimal places you wrote are the decimal places used and the arithmetic stays in whole numbers. The trade-off is that it only handles terminating decimals — which is the case that arises in practice: a measurement of 0.625 in, a price of 12.99, a probability of 0.05, a gear ratio of 2.35. Number Base Converter shows exactly why binary struggles with decimal fractions, and GCF/LCM Calculator is the machinery behind the reduction step if you want to verify it by hand.

Private and instant

The maths runs entirely in your browser. Nothing is uploaded and no account is needed.