0.999... is also an 'exact' number (being the same number, 1).
how?
Infinity goes on forever.
That's the answer really. Each consequtive 9 decreases the difference between the number and 1 by a factor of 10. You do this infinite times and you've decreased the difference by a factor of infinity; i.e. there is 0 difference.

I think you're asking at what point leading up to infinity is it 0; there is no point. That's the whole point of infinity, it isn't a number as such. It just represents what would happen if you did it again and again and again forever. You can't in practice, but it's just a concept.

The above is all intuitive however. The real answer to your question is simply the mathematical proofs which have been offered. Mathematics is abstract. Think what would happen if you tried to discuss the Banach–Tarski paradox in this way; it doesn't work.