Correction: Bitcoin is 8-digit fixed-point. But Lightning is 10, IIRC. Other currencies have different conventions. Still, it's fixed within a given system and always fixed-point. As far as I'm aware, there are no floating-point cryptocurrencies at all, because it would be an obvious exploit vector - keep withdrawing 0.000000001 units from your account that has 1.0 units.

How does this avoid rounding error? Division and multiplication and still result in nonrepresentable numbers, right?

It is not hard to remember what int division is about, when your types are ints in code. It also comes up almost never, and isn't what floating-point rounding error means. You aren't multiplying money 99% of the time, and when you are, you don't care about exacting precision (e.g. 20% discount). Floating-point rounding error, on the other hand, is about how 0.1 + 0.2 != 0.3.