Free Decimal to Fraction Calculator

Last updated September 24, 2026 · Report an error

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Every real number that has a decimal representation with a finite number of digits — a "terminating" decimal like 0.75 — converts directly to a fraction over a power of 10. Every decimal that instead settles into an endlessly repeating block of digits, like 0.3333... or 0.1666..., is also a rational number and converts to a fraction too, just via a different algebraic technique (multiplying by a power of 10 to shift the repeating block, then subtracting to eliminate it entirely). Converting decimals to fractions is essential whenever exact values matter more than decimal approximations: doing exact arithmetic by hand or in a spreadsheet formula that needs a precise fraction rather than a rounded decimal, working with measurements in engineering and carpentry that are conventionally expressed in fractions of an inch, and verifying textbook or exam answers where a decimal approximation like 0.333 needs to be recognized as exactly 1/3.

How it works

Enter a decimal. For a purely terminating decimal, the calculator writes it directly as (the digits after the decimal point) over the matching power of 10 — for example, 0.75 becomes 75/100 — and then simplifies using the greatest common divisor (GCD). For a repeating decimal, enter the repeating block in parentheses right after any non-repeating digits (e.g., 0.1(6) means 0.16666... forever). The calculator applies the standard algebraic elimination technique: it sets up an equation for the decimal, multiplies both the non-repeating and full parts by the appropriate powers of 10 to align the repeating blocks, subtracts one equation from the other to cancel the infinite repetition entirely, and solves for the exact fraction, before simplifying with the GCD.

Enter decimal (use parentheses for a repeating block, e.g. 0.1(6)).
Click Calculate to see your results.

Examples

0.75

75/100 simplifies (dividing by their GCD of 25) to 3/4.

0.(3)

A purely repeating decimal (0.333...): (3−0)/(10−1) = 3/9, which simplifies to 1/3.

0.4(6)

A mixed terminating-then-repeating decimal (0.46666...): using the full algebraic elimination formula, (46−4)/90 = 42/90, which simplifies to 7/15 — and indeed, 7 ÷ 15 = 0.46666....

Common mistakes to avoid

Treating a repeating decimal as if it were terminating, which gives an inexact fraction that only approximates the true value rather than matching it exactly.
Forgetting to simplify the resulting fraction using the GCD, leaving an unnecessarily large numerator and denominator.
Placing the parentheses around the wrong digits, accidentally marking a non-repeating digit as part of the repeating block (or vice versa).
Assuming every decimal, including irrational ones like π, can be converted to some fraction — only rational (terminating or repeating) decimals actually can.

Frequently asked questions

Put the repeating digits in parentheses right after the non-repeating part, e.g. 0.1(6) for 0.16666..., or 0.(3) for 0.3333... with nothing repeating before the block starts.

A fraction in lowest terms produces a terminating decimal if and only if its denominator's only prime factors are 2 and/or 5 (like 1/8 = 0.125, since 8 = 2³); any other prime factor in the denominator (like 3, 7, or 11) guarantees the decimal repeats eventually.

Multiplying the decimal by the right power of 10 shifts the decimal point so that the repeating block lines up exactly with itself in the original number. Subtracting the two equations then cancels the infinitely repeating part completely, leaving a simple, solvable equation with only a finite number of terms.

Yes — applying the same elimination technique to 0.(9) gives (9−0)/(10−1) = 9/9 = 1 exactly, a famous and sometimes counterintuitive but mathematically rigorous result.

You get an inexact fraction that only approximates the true value — for example, treating 0.333 (three digits) as terminating gives 333/1000, which is very close to but not exactly equal to the true value of 1/3.

Only decimals that either terminate or eventually settle into a repeating pattern — these are exactly the rational numbers. A decimal that goes on forever without ever repeating (like π = 3.14159... or √2) is irrational and has no exact fraction representation at all.