To answer the title, it does. I don't remember the proof exactly, but I think it was this.

1/9 = 0.1111...
=> 10/9 = 1.111...
=> 90/9 = 9.999...
=> 9/9 = 0.9999...
=> 1 = 0.9999...

Or something like that. This exact wording actually doesn't hold up because the first line assumes that my conclusion is already correct...