Fraction to decimal

What it's for

A fraction says one thing only: divide the number on top by the one underneath. You need it when a number arrives written as a fraction but you need it as a decimal, which is nearly every practical case: a measurement to mark on a tape, a ratio to put in a spreadsheet, a mark, a quantity to weigh on scales, reading a half-inch spanner.

The point school tends to skip

Not every fraction gives a decimal that ends. 3/4 is 0.75 and stops; 1/3 is 0.333… and never stops. The rule for knowing in advance is precise: reduce the fraction to its lowest terms and look at the denominator. If it contains only the factors 2 and 5 (2, 4, 5, 8, 10, 16, 20, 25, 40…) the decimal ends; if it contains any other prime factor (3, 7, 11, 13…) the decimal repeats, going on forever with a recurring group of digits.

Here the result is shown with at most eight digits after the point, so a repeating decimal appears cut short: 1/3 shows as 0.33333333 and 1/7 as 0.14285714. That isn't a calculation error, it's that the exact number can't be written out in full. If you need the exact value, the fraction itself is the right place for it.

The fractions you actually meet

1/2 = 0.5 · 1/3 = 0.333… · 1/4 = 0.25 · 1/5 = 0.2 · 1/8 = 0.125 · 2/3 = 0.666… · 3/4 = 0.75 · 1/16 = 0.0625. Powers of two (half, quarter, eighth, sixteenth) always give decimals that end, which is why they're used in inch measurements and in recipes: you can halve them as many times as you like without ever losing anything.

Nearby tools

The opposite direction, from a decimal to the simplest fraction that represents it, is Decimal to fraction. To work out a fraction of a quantity («three quarters of 240») there is Fraction of a number, and to turn the fraction into a percentage Percentage calculator.