Why do you estimate in math?

Answer 1

In the real world sciences, there are limits to how precisely we can measure quantities, weights, time, temperature etc. It is impossible to give answers that are not estimates.

In computer science, there is a limit to how many decimal places the computer (or calculator) can hold. So numbers have to be rounded.

In pure math, many numbers are irrational and transcendental (pi for example). If you were to try writing them out, you would have a decimal that goes on forever without repeating. You would spend an eternity simply trying to write out one number.