Q&A #7093

Teachers' Lounge Discussion: Converting repeating decimals to fractions

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From: Allen Robinson

To: Teacher2Teacher Public Discussion
Date: 2016100615:06:11
Subject: Re: Converting 0.9(repeating) to a fraction.

The closest fraction to 0.9 (repeating) is 10^&#8734;-1/10^&#8734; What I mean by this is subtracting 1 from 10 to the power of infinity would produce an infinite number of 9's. dividing this by 10 to the infinite power (1000000000000000000000000...) makes 99999999999999.../100000000000000... still a fraction while retaining it's repeating state. Other simplifications are 1 - 10^-&#8734;.

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