I assume you are alluding to CONTINUED fractions? Many irrationals have a simple repetitive continued fraction representation, and even 'e' has a regular pattern, even though it doesn't actually repeat. And of course any finite continued fraction is a simple fraction, and can be represented by a repeating decimal.
“I assume you are alluding to CONTINUED fractions?”
Well, yeah I wasn’t really clear on that point, maybe I should have left it off. What I meant, in terms of Pi, is that it looks irrational written as a decimal, but in fact, the only reason it is a significant number to us is because it’s the decimal approximation of a ratio. That ratio isn’t one between two whole numbers, that might produce a repeating fraction, but between two related geometric quantities.
So, if one theoretically constructed a number system using some geometric base rather than our arithmetic one, Pi would be completely rational, and could be approximated exactly. So, I think it’s all a matter of perspective.