Ah, to be seeing this for the first time.
We have
[tex]x = 0.999999999...[/tex]
So
[tex]10x = 9.99999999...[/tex]
Subtracting,
[tex] 9x = 9[/tex]
[tex]x = 1[/tex]
Answer (as a fraction): 1/1
That's not an approximation; 0.9999... is exactly equal to 1.
