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Q&A #7093


Converting repeating decimals to fractions

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From: Jeanne (for Teacher2Teacher Service)
Date: Oct 19, 2001 at 19:13:03
Subject: Re: Converting repeating decimals to fractions

Hi Robert,

Here is one of the conversion methods I teach to my high school students.

Let N = 0.66666...

If N = 0.66666..., then 10N = 6.66666...

We can subtract 10N - N as follows:
           10N = 6.66666...
         -   N = 0.66666...
        --------------------
            9N = 6

Therefore, N = 6/9 which reduced to lowest terms equals 2/3.

Thus, 0.66666..... = 2/3 .

Hope this helps.

 -Jeanne, for the T2T service

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