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Old 10-29-2003, 09:38 AM   #12 (permalink)
dimbulb
Riiiiight........
 
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
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
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