Comment by Sharlin

If you believe that real numbers are numbers, then, yes, pi is a number. Indeed because pi is computable, it’s actually "more" real than almost all real numbers because there is only a countable infinity of computable reals.

Anyway, in modern math what a real number is, is defined as the limit of a "process", namely a Cauchy sequence. Of course, for the rational subset of reals the limit is trivial.