Hmm, yes, it can be represented in ASCII. But you still have to approximate when storing it in a way that is actually useful for computation using a finite number of bits.
Many real programming languages support arbitrary precision decimal and/or rational numbers.
Sure, there are times when space or speed concerns favor inexact representation over correctness, but that's an optimization that ought to be properly evaluated; the fact that lots of languages are designed in a way which makes it the default everyone reaches for contributes to lots of errors.