You can only store rational numbers as a ratio of two numbers, and there's infinitely times more irrational numbers than rational ones - as soon as you took (almost any) root or did (most) trigonometry, then your accurate ratio would count for nothing. Hardcore maths libraries get around this by keeping the "value in progress" as an expression for as long as possible, but working with expressions is exceptionally slow by computer standards - takes quite a long time to keep them in their simplest form whenever you manipulate them.