Quote:
Originally Posted by Lisasmith111
Mr Hui,
I think this one becomes 1 as the following illustrates:
let x = 0.999 and 10x = 9.999
10x  x = 9
9x = 9
x = 1
0.999 is approx = 1 (I guess there has to be some rounding at due to the nature of decimals, whereas fractions can be more exact.

Lisa, there is no rounding involved. 0.999999999... is exactly equal to 1 by the reasoning you showed. If x = 0.99999999... and 10x = 9.999999... then when you subtract x from 10x, it cancels out all of the 9's to the right of the decimal point.
10  x = 9.999999...  0.99999999...
9x = 9
x = 1
Substituting back gives 1 = 0.99999...