[Isognoviastoma]

- after few operations denominator exceeds 64-bit range, so you either need bigint, or make fractions approximate, what is in affect fixed point

- often you use decimal fraction on output and input anyway

- it's slower, even slower with bigint

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

[lifthrasiir]

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

Better statement would be "no standard definition possible for square root, sin, and so on with rationals", as rationals with unbounded denominators don't have an inherent precision limit---something like ulps in floating point systems---and the max denominator wouldn't be a good choice for precision even when denominator is limited. Every such function now has to be given an explicit denominator value or similar strategy, which complicates both the interface and implementation.

[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.