If you needed ten billion dollars, and had $9,999,999,999.00 do you have ten billion dollars? 
I think the answer "infinitely close to one in the base ten system" might be the best.
One problem I could see is looking at a situation where X has to be a number equal to or greater than one, X >/= 1. 0.9999999999... would not be greater than or equal to x in that case.
It would be more like if you had $9,999,999,999.99999.... The problem with your example is that you are short by an amount that is defined as $1, a non-zero value. In the topic's question, 0.99999999... is short by an infinitely small amount, which is mathematically defined as 0. You see what I mean?
I question if yo can really define this as zero, anymore than can define it as 42.
For example: X is defined the amount of molecules of a substance needed for a reaction, and the amount of X needed is 1 unit. 0.999999999... units would not be enough.
So long as X isn't a minimum amount, the definition would work. As soon as it becomes a minimum value, there is a definitional problem.
0.9999999999.... is 1, and it's statistically significant.
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