We have lots of ways to notate numbers. "2/3", for example, is a perfectly good notation for the number you get when you divide 2 by 3.
Decimal notation for real numbers is taught because:
- It's simple
- It fits well with decimal notation for integers
- It's very easy to trade precision for simplicity. (e.g. just write the first few digits)
Most people don't have any reason to learn notations other than a mix of algebraic expressions with decimals.