[Isognoviastoma]

√2 with floating point is obviously closest representable number. With fixed point it is obviously closest representable number as well. With rationals, you need to arbitrarily limit precision, and the point of using rational was to use exact values.

[User23]

Rational approximation is a thing. 22/7 and all that.

[NL807]

I don't think that's a big deal though. You deliberately choose to use a rational system, because you understand the problem domain, which could greatly benefit from such a representation. If you throw a rational system at every math problem as a catch-all representation, then you are doing it wrong.