Decimal to fraction

What it's for

A number with a decimal point doesn't always say what you need. 0.375 brings nothing to mind; written 3/8 it's a spanner size. In the kitchen 0.25 of the cream is a quarter, in music 0.125 is an eighth, in a workshop inch measurements are all fractions. Here the decimal goes back to its fraction form, already reduced to lowest terms.

How it's done

The decimal is written as a fraction whose denominator is a power of ten, one for each digit after the point, and then it's simplified by dividing top and bottom by the greatest common divisor: 0.75 becomes 75/100, which simplified is 3/4. It's exactly the method taught at school, done without writing out the steps.

The thing to know: decimals that never end

A repeating decimal, like 0.333…, can't be written out in full, so what you type here is always a cut-short version. If you type 0.333 the correct answer is 333/1000, not 1/3: they're two different numbers, and the page gives you what you actually typed, not what you meant to type.

It's worth knowing the common ones, because you can recognize them by eye and fix them in your head: 0.333… is 1/3, 0.666… is 2/3, 0.1666… is 1/6, 0.142857… is 1/7. If the number you have starts like that, the fraction you're after is that one, not the one the truncation produces.

Nearby tools

The opposite direction is Fraction to decimal, which also explains which fractions give a decimal that ends and which don't. To work out how much a part of a quantity is worth there is Fraction of a number, and to keep only the digits you need Round a number.