Maybe it's a matter of notation although I think O.111... is a recognised abreviation for 0.1 recurring. Would O.(1) be better? I don't think it's an approximation. Pi written out to a trillion places of decimals would be an approximation but 0.(1) doesn't mean 0.111... written out to a trillion places of decimals, it means written out to an infinite number of decimal places. Infinity doesn't just mean a very big number. As far as I can see, 1/9 is exactly equal to 0.(1). Just because you can't write it out in full doesn't mean it isn't true.

Others can argue this better than me - http://en.wikipedia.org/wiki/0.999%E2%80%A6