Fraction to decimal calculator

Type a fraction like 5/8, or a mixed number like 1 2/3 with a space before the fraction. The decimal appears straight away, with the long division that produced it, a rounded version, the percentage, and fraction bars. Tops and bottoms up to a million work.

When the decimal repeats, the repeating digits are marked with a bar, as in 0.16̅ for 1/6, and also given in brackets, 0.1(6), which is easier to type elsewhere. However long the repeating block is, the calculator finds exactly where it starts.

A fraction is a division, so 5/8 means 5 ÷ 8. Since 8 doesn't go into 5, write 0 and a decimal point, bring down a 0 to make 50, and divide. 8 goes into 50 six times with 2 left over, so the first digit is 6. Bring down another 0 to make 20, which gives 2 remainder 4, then 40, which gives 5 remainder 0. When the remainder is 0, the decimal ends, at 0.625.

Sometimes the remainder never reaches 0. For 1/6, the remainders go 4, 4, 4… and each one gives another 6. Since there are only so many remainders smaller than the bottom number, one must come round again eventually, and from then on the digits repeat. That's why every fraction gives a decimal that either ends or repeats.

Simplify the fraction first, then factor the bottom. If its only prime factors are 2 and 5, the decimal ends, as 3/8, 7/20 and 9/125 do. Any other prime makes it repeat, so 1/3, 1/6, 1/7 and 1/12 all go on for ever. The repeating block can be long, since 1/7 repeats every 6 digits, and 1/97 every 96.