naipotato/0.30000000000000004

Floating Point Math Examples

0.30000000000000004.com

Floating Point Math

Your language isn't broken, it's doing floating point math. Computers can only natively store integers, so they need some way of representing decimal numbers. This representation has a degree of inaccuracy which is why, more often than not, 0.1 + 0.2 != 0.3.

Why does this happen?

It’s actually rather interesting. When you have a base-10 system (like ours), it can only express fractions that use a prime factor of the base. The prime factors of 10 are 2 and 5. So 1 / 2, 1 / 4, 1 / 5, 1 / 8, and 1 / 10 can all be expressed cleanly because the denominators all use prime factors of 10. In contrast, 1 / 3, 1 / 6, and 1 / 7 are all repeating decimals because their denominators use a prime factor of 3 or 7.

In binary (or base-2), the only prime factor is 2, so you can only express fractions cleanly which only contain 2 as a prime factor. In binary, 1 / 2, 1 / 4, 1 / 8 would all be expressed cleanly as decimals, while 1 / 5 or 1 / 10 would be repeating decimals. So 0.1 and 0.2 (1 / 10 and 1 / 5), while clean decimals in a base-10 system, are repeating decimals in the base-2 system the computer uses. When you do math on these repeating decimals, you end up with leftovers which carry over when you convert the computer's base-2 (binary) number into a more human-readable base-10 representation.

Below are some examples of sending .1 + .2 to standard output in a variety of languages.