I don't think you are quite getting the calculation.
We set x to 0.999... (reoccuring). 10x is therefore 9.999... (simple multiplication).
To get 9x, we need to subtract x from 10x (10x - x), which is the same as doing the calculation 9.999... - 0.999...
So 9x = 9
So x = 1.
The calculation is explained in more detail here: http://en.wikipedia.org/wiki/0.999...
0.999... is a real number equal to one.
We set x to 0.999... (reoccuring). 10x is therefore 9.999... (simple multiplication).
To get 9x, we need to subtract x from 10x (10x - x), which is the same as doing the calculation 9.999... - 0.999...
So 9x = 9
So x = 1.
The calculation is explained in more detail here: http://en.wikipedia.org/wiki/0.999...
0.999... is a real number equal to one.