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.
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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...