Yeah there are a few number systems that can do this kind of thing, ranging from rational implementations where the numerator and denominator are stored, all th

Yeah there are a few number systems that can do this kind of thing, ranging from rational implementations where the numerator and denominator are stored, all the way to the computable reals (https://en.wikipedia.org/wiki/Computable_number https://en.wikipedia.org/wiki/Computable_number), which can handle even trancendentals exactly! Fun fact, the built-in calculator on android actually uses the computable reals (https://dl.acm.org/doi/abs/10.1145/3385412.3386037 https://dl.acm.org/doi/abs/10.1145/3385412.3386037), so you can do any calculation on it, and then ask for any number of digits (keep scrolling the result), and it will always be correct. The only downside is that they're a little too slow to use in a lot of performance-sensitive numerical applications.