A float always precisely represents a specific number, but that number is not always precisely the equal to the algebraic result of the operations performed (even when ignoring transcendental and irrational functions). This should be obvious since there is no limit to rational numbers, but finite floating point numbers.

If you design your algorithms very carefully, you can end up with the ratio of the output of your algorithm to the ratio of the algebraic result close to unity over a wide domain of inputs.