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Math Help - 0.999... = 1?

  1. #1
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    Post 0.999... = 1?

    I can't seem to figure out what I am doing wrong

    express in form a/b

    0.9 (bar)

    So I start...

    x = 0.99999...
    10x = 9.9999...

    LHS:
    10x - x = 9x

    RHS:
    9.9999 - 0.9999 = 9

    so 9x = 9

    thus x = 1

    So now I am stuck and can't seem to figure out where I went wrong... plz help
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Solan View Post
    I can't seem to figure out what I am doing wrong

    express in form a/b

    0.99 (bar)

    So I start...

    x = 0.99999...
    10x = 9.9999...

    LHS:
    10x - x = 9x

    RHS:
    9.9999 - 0.9999 = 9

    so 9x = 9

    thus x = 1

    So now I am stuck and can't seem to figure out where I went wrong... plz help

    That is correct for that method. Another way is this

    .9999=\frac{9}{10}+\frac{9}{100}+\frac{9}{1000}+..  .=\sum_{n=0}^{\infty}\frac{9}{10^{n+1}}

    \frac{9}{10}\sum_{n=0}^{\infty}\frac{1}{10^n}=\fra  c{9}{10}\cdot \frac{1}{1-\frac{1}{10}}=\frac{9}{10} \cdot \frac{10}{9}=1

    Good luck.
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  3. #3
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    mr fantastic's Avatar
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    Quote Originally Posted by Solan View Post
    I can't seem to figure out what I am doing wrong

    express in form a/b

    0.9 (bar)

    So I start...

    x = 0.99999...
    10x = 9.9999...

    LHS:
    10x - x = 9x

    RHS:
    9.9999 - 0.9999 = 9

    so 9x = 9

    thus x = 1

    So now I am stuck and can't seem to figure out where I went wrong... plz help
    You're not wrong. So the answer to the question is 1/1.
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