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Teachers' Lounge Discussion: Converting repeating decimals to fractions

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From: Tony

To: Teacher2Teacher Public Discussion
Date: 2003031414:02:26
Subject: Converting 0.9(repeating) to a fraction.

Okay, so this came up in one of my math classes:  if you use the
technique above to convert 0.99999999... to a fraction, you find it to
be identical to one.  
             x = 0.99999.......
           10x = 9.99999.......
        So, 9x = 9, which means x = 1.
While the two numbers may be infinitesimally close, they are not
identical.  Is there something wrong or incomplete about the
technique?

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