I think the validity of the use of the real numbers depends on whether space is continuous or discrete, or whatever it is. I don't know of a way to prove either or. But definitely the popular notation of Writing Real Numbers as Neverending Trailing Decimal expansions is quite pointless as those numbers can't be written in decimal. Same for some rational decimal expansions. Since you can't split something into 3 parts without a remainder if it is not already a multiple of 3. In decimal, the base isn't a multiple of 3 so if you divide 1 by 3, you should always have a remainder after the division. the unending length of 3s that is commonly used would never equal 1/3 as it would be impossible to write 1/3 using a decimal expansion because there is always a remainder as a result of that division.