[crabbone]

> no square root, sin, and so on with rationals

Are you thinking about a specific library? You aren't the only person who commented this way. But, the truth is that root, sin and so on don't "work" with floats either. In fact, there are common ways to implement these functions by either using tables (which are approximate) or algebraic approximations (that give you... drum roll: rationals!)

But, really, there isn't any way (except symbolically) to represent transcendental functions in computers. It doesn't matter what kind of number you choose to do it.

[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.