this post was submitted on 17 Sep 2023
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Computers are binary, yeah? So we have to represent fractional numbers with binary, too.
In decimal, numbers past the decimal point are 10^-1, 10^-2, ... etc. In binary, they're 2^-1, 2^-2, ....
2^-1 is one half, so 0.1 in binary is 0.5 in decimal. 2^-2 is one quarter. 0.11 in binary is 0.75 in decimal. And of course you've got 0.01 = 0.25
The problem comes when representing decimal numbers that don't have neat binary representations. For instance, 0.1 in decimal is actually a repeating binary number: 0.0001100110011...