We could just use 2 integers for floats and not deal with inaccuracies. Even easier.

Floats can represent faaar bigger span than two integers. 2*10^-308 to 2*10^+308 is gonna require you 1024 bits or 32 integers. Now those 32 integers would represent that value exactly instead of rounding a few decimals, but some maths prefer approximate large span over exact values.