Quote:
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Originally Posted by Alan Anderson
".9999 continuing" is equal to 1.
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Quote:
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Originally Posted by sanddrag
How do you figure? You are always going to have that really small (but existant) 0.00000...00001 left over. I see 0.999 continuing as approaching 1 but I am inclined to think it never actually gets there.
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Your position is based on the false impression that the 9s eventually run out, leaving a bit left unaccounted for. They don't; that's what repeating decimals are all about.
Figuring it is easy:
Code:
x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1
See also
http://en.wikipedia.org/wiki/Recurri..._of_0.99999... for other ways to demonstrate it.