All possible numerical representations come with inherent trade-offs around speed, accuracy, storage size, complexity, and even the kinds of questions one can ask (it's often not meaningful to ask if two floats equal each other without an epsilon to account for floating point error, for instance).
"Toward an API for the Real Numbers" ( https://dl.acm.org/doi/epdf/10.1145/3385412.3386037 ) is one of the better papers I've found detailing a sort of staged complexity technique for dealing with this, in which most calculations are fast and always return (arbitrary precision calculations can sometimes go on forever or until memory runs out), but one can still ask for more precise answers which require more compute if required. But there are also other options entirely like interval arithmetic, symbolic algebra engines, etc.
One must understand the trade-offs else be bitten by them.