If you have integers that are stored in floating point types and don't need more than [mantissa] bits of precision, you can operate on them like ints and always* get the right result. Nobody would expect that the formula `return new_maxhp * (old_hp / old_maxhp);` would work with ints, but they see floats as magic that allow them to drop their guard about precision and rounding of operations. Unfortunately not.

Rationals have a big problem where under multiplication and division they need to be re-normalized periodically, and that re-normalization is slow (running gcd). Under addition and subtraction, rationals are great.

*the one big difference is that division rounding is different