Every option here has tradeoffs and drawbacks: fixed point arithmetic suffers from a very limited precision range, rationals aren't even the same number set, cauchy sequences are precise but comparatively very slow… there's no one size fits all solution that's right in every circumstance.
Except, of course, at lower levels of abstraction - where IEEE floats are what the hardware implements. Lower level languages use 8-, 16-, 32-bit integers, they use IEEE floats and doubles, and they make these choices for pretty solid reasons.
Higher level languages make different choices (arbitrary precision integers are common in interpreted languages, eg). Libraries support all kinds of options up and down the stack.
