Fraction to Decimal Converter

Every value is exact: one inch is defined as exactly 25.4 millimeters. Sixty-fourths cover the full range of imperial drill and fastener sizes.

A fraction in lowest terms terminates as a decimal only if its denominator factors into twos and fives alone, because ten is two times five. Halves, quarters, fifths, eighths, tenths, sixteenths and sixty-fourths all terminate. Thirds, sevenths, ninths and elevenths repeat forever.

That is why every inch fraction in the table above has an exact decimal: the denominators are all powers of two. It is also why a third of an inch does not appear on any spanner.

Imperial sizes step in sixty-fourths at the small end and sixteenths higher up, which is why a set of drill bits reads 1/16, 5/64, 3/32, 7/64, 1/8. Converting each to millimeters shows how close some pairs are: a 5/16 inch bit is 7.94 mm and sits between an 8 mm and a 7.5 mm.

That closeness is the trap. A 13 mm spanner will turn a 1/2 inch bolt head at 12.7 mm, badly, and will round the corners off it. Check the millimeter column before assuming two sizes are interchangeable; anything under about 0.2 mm apart is usually fine, and more than that is not.

All three notations describe the same ratio. Percent literally means per hundred, so 37.5 percent is 37.5/100, which reduces to 3/8. Moving between them is a division and a multiplication by 100, in one order or the other.

To go from a decimal back to a fraction, write the digits over the matching power of ten and reduce: 0.375 is 375/1000, which divides top and bottom by 125 to give 3/8. Repeating decimals need a different method and rarely reduce to anything tidy.