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

  1. #16
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    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...
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  2. #17
    Grand Panjandrum
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    Quote Originally Posted by Quick View Post
    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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