That is something I would be interested in, I always assumed arbitrary precision arithmetics would also have to turn one third into some finite approximation, t

That is something I would be interested in, I always assumed arbitrary precision arithmetics would also have to turn one third into some finite approximation, though you can choose however much precision you need or want. I ran across this once when I implemented a rational number type with arbitrary precision integers and wanted to print the decimal representation. I wanted to determine the repeating and non-repeating fractional parts but failed to find any applicable math or algorithm. If I am not misremembering and did not do my research to poorly, this is an open problem and at best you can start expanding and look if you return to a state you were in before. But at some point you have to give up because you can not event determine the length of the repeating and non-repeating fractional parts in advance and even some relatively small numerators and denominators can produce some pretty long decimal representations until they start repeating.