The trouble you have is that you really wanted reals and the rationals are not a much better substitute than the floats (which are mostly just one particularly specialised flavour of rational)

It doesn't feel immediately like there ought to be a problem, but witness, mathematically almost all of the reals are Normal and unfortunately Normal doesn't mean "normal" it's a technical mathematical word, that for our purposes means roughly "completely batshit".

Normal numbers are non-computable, so we definitely don't want to try to use them in software, which is a problem because again, almost all of the reals are Normal.