@me1958424 did you mean, that you can get a fraction a/b as small as you want, while it still would be repeating a sequence of digits?
In that case, you can, it is even extremely simple; just write any natural number and repeat its digits infinitely…
But, that wouldn’t have any of the nice properties, that fractions have.
For instance: 1/7 = 0.142857…, like we already established, but multiplying this by a natural number, cycles through those digits!
2/7 = 0.285714… 5/7 = 0.714285… and so on.
You would not have something like this, when you’d divide one of those infinitely large numbers.
The thing is, I think, that those large, repeating numbers are constructed, while the fractions repeat naturally….I hope that makes some sense to you 🙂
