I like rational numbers in general, but they do have some huge practical issues in numerical algorithms. In particular, there's no upper bound on the memory use

I like rational numbers in general, but they do have some huge practical issues in numerical algorithms. In particular, there's no upper bound on the memory use of a rational based on its magnitude. Following from that, there's no lower bound on the time an arithmetic operation may take based on the magnitudes of the operands. When you're doing hundreds of thousands of operations on an accumulator, this can go very wrong. So I caution against blind preference for rational representations as well. You really have to choose your numeric representation based on your use case. It's unfortunate that this can be so hard to control precisely in many programming languages.