How to Convert a Fraction to a Decimal

A fraction is just a division waiting to happen. The line between the numerator and denominator means 'divided by', so to turn a fraction into a decimal you divide the top number by the bottom number. Three-eighths is 3 divided by 8, which equals 0.375.

That single rule covers every fraction. Whether the numbers are small like 1/4 or awkward like 7/16, the decimal is always the numerator divided by the denominator. The only question is whether the division ends cleanly or runs on forever.

Some fractions divide evenly and stop — these are terminating decimals, like 3/8 = 0.375 or 1/4 = 0.25. A fraction terminates when its denominator, in lowest terms, has no prime factors other than 2 and 5, the factors of ten.

Other fractions never resolve and a digit or block of digits repeats forever. One-third is 0.333…, written 0.(3), and five-sixths is 0.8333…, written 0.8(3). The parentheses mark exactly which digits recur. The calculator detects the repeating block automatically so you don't have to spot the pattern by hand.

When a fraction doesn't convert in your head, long division gets you there one digit at a time. The calculator writes out each step, but here is the process so the answer makes sense.

To convert a terminating decimal back into a fraction, write the digits over the matching power of ten and simplify. 0.75 is 75/100, which reduces to 3/4; 0.375 is 375/1000, which reduces to 3/8.

Repeating decimals need a bit more algebra to convert exactly, but the common ones are worth memorizing: 0.(3) is 1/3, 0.(6) is 2/3, and 0.(142857) is 1/7. The converter handles terminating decimals precisely and reduces them to lowest terms for you.