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, and the page writes out the steps under the result.

The thing to know: decimals that never end

A repeating decimal, like 0.333…, can't be written out in full, but it can be written with the repeating part in brackets, which is what you do in an exercise book when you can't draw the line over it: 0.(3) is 1/3, 0.1(6) is 1/6, 2.(45) is 27/11, and under the result the page shows the rule it used, with its numbers. If instead you type 0.333 the answer is 333/1000, not 1/3: they're two different numbers, and the page gives you what you actually typed.

When a decimal ends with three equal digits, like 0.333 or 0.1666, the page points it out and tells you what it would be with the repeating part. It's still worth knowing the common ones, because you can spot them by eye: 0.333… is 1/3, 0.666… is 2/3, 0.1666… is 1/6, 0.142857… is 1/7.

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. To reduce a fraction to lowest terms with the steps, or to add, subtract, multiply and divide two fractions, there is Simplify Fractions.