The problem comes when you need to mix precision and now all your multiplication and division needs to keep track of the decimal point through the computation.

The problem comes when you need to mix precision and now all your multiplication and division needs to keep track of the decimal point through the computation. This isn't terribly uncommon, usually when your computation needs much wider range than your input and output. Exponentials and logarithms are bad about this. So what you do is either keep track of the precision manually in your call stack, but then you get the bright idea to pass it as data along with your integer. And you don't need 64 bits of precision because that's a lot, you can live with 52 and use the extra bits to hold your exponent. And lo and behold you've discovered floating point.