How can we use irrational numbers in math if we don’t know the full number?

Question

How can we use irrational numbers in math if we don’t know the full number?

In: 232

Answer 1

Most fields do not require a fully exact value to be used. For example, for most applications that use Pi, they only need like 5-10 digits of it (and for rough calculation, just the “3.14” part is often enough).

Besides, there’s a separate but related concept called “precision”. In actual physical measurements there’s always some degree of error, which “precision” is the measure of. Mathematical approximations of irrational numbers should be a few digits more exact than the imprecise measures, but any more than that is really not necessary because it introduces false precision into the result.