Quote:
Originally posted by Jakejake
Let x = 0.999999....
10x = 9.9999999.........
10x - x = 9.99999........ - 0.999999....
10x -x = 9
9x = 9
x = 1
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nice one...
you can pretty much do this for any decimal expansion that is periodic.
A corollary is that any decimal expansion that is periodic can be expressed as a rational number ( fractions for the rest of us... )
like x = 0.73737373737373......
with period n, in this case 2,
(10^n)x = 73.7373737373.....
(10^n)x - x = 73
x = 73/(100-1)
x = 73/99