The original question is pretty stupid, since there is no physical way for time to be measured to an infinite series of decimals. Every measuring device ever made by man counts up by a certain increment, and there is inevitably some space between those increments. .9 repeating would fall into the space between .9999 (to however many digits are measured) and 1.
And yes, .9 repeating does in fact equal 1. It's hard to understand, so you sort of just have to take it as being true. One way to think about this is that there is no value, however small, that can be added to .9 repeating to give you 1. Thus, the two must be the same. Or, if you need a proof:
x=.99999999999999...
10x=9.99999999999...
10x-x=9.9999.... - .999999....
9x=9
x=1
Really, you have to take a step back and think of it as being a value, with a set place on the number line. That value cannot be getting closer and closer to 1, it has a set position. If you try to mark it down as .9999999 or even .9999999999999, its not there. There are no numbers on the number line betweent .9 repeating and 1, so the two must therefore be equal.