# Math Help - 0.99999999999........=1

1. Originally Posted by CaptainBlack
Tell us how you do the addition:

0.666.. + 0.333..

to get 0.999..?

RonL
well, here's how you do it to $n$ decimal places...
$6\times 10^{-1}+6\times 10^{-2} +....6\times 10^{-n} +3\times 10^{-1}+3\times 10^{-2} +....3\times 10^{-n}$

$=(3+6)\times 10^{-1}+(3+6)\times 10^{-2} +....(3+6)\times 10^{-n} =0.99...$

2. Originally Posted by Quick
well, here's how you do it to $n$ decimal places...
$6\times 10^{-1}+6\times 10^{-2} +....6\times 10^{-n} +3\times 10^{-1}+3\times 10^{-2} +....3\times 10^{-n}$

$=(3+6)\times 10^{-1}+(3+6)\times 10^{-2} +....(3+6)\times 10^{-n} =0.99...$
That only gives you n nines not ... nines. You need to take the limit
as n becomes arbitarily large, but that is 1.

RonL

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