Why aren't repeating decimals irrational but something like $pi$ is?

We use closest representations for both of them, but they are not completely true.

$\frac{22}7$ and $3.14$ are not exactly $\pi$ but we use them as the best option available.

$\frac13$ is $0.\bar3$ but that can be $0.333$ or $0.333333$ and these are not equal.

So why is one irrational and other is not?