Maybe a stupid question, but can you even divide a number with infinite decimals?

I know you can find ratios of other infinitely repeating numbers by dividing them by 9,99,999, etc., divide those, and then write it as a decimal.

For example 0.17171717.../3

(17/99)/3 = 17/(99*3) = 17/297

but with 9 that would just be... one? 9/9=1

That in itself sounds like a basis for a proof but idk