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# erikwiffin / 0.30000000000000004

Floating Point Math Examples

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# 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.

Floating Point Math Examples

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