I'm not a mathematician, but this is always the way I've looked at it too.
We can't represent values like 1/3 precisely in the decimal number system, the best we can do is represent in a way that it's clear what's implied with minimal error.
The representation isn't really suppose to be interpreted as an infinite decimal series, and depending on how you interpret 3.333... you could argue it's a slightly different value. And that's plainly obvious – 3.333... != 1/3
We can't represent values like 1/3 precisely in the decimal number system, the best we can do is represent in a way that it's clear what's implied with minimal error.
The representation isn't really suppose to be interpreted as an infinite decimal series, and depending on how you interpret 3.333... you could argue it's a slightly different value. And that's plainly obvious – 3.333... != 1/3