We can tell that $$0.11111111... \cdot 9 = 0.999999999...$$ And that $$\frac19 = 0.11111111111...$$
Therefore $$\frac19\cdot9 = 0.999999999...$$
However, we know that $$\frac19\cdot9 = \frac99 = 1$$
Note: I'm taking in account that ... are the other rational digits left.
What am I making wrong? What is misunderstood?
Thanks for the help in clearing this problem.