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Express 0.\overline{2123} as a base 10 fraction in reduced form.

 Jun 13, 2024
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We want to convert \( 0.\overline{2123} \) into a fraction, and we can do this with a very handy trick. 

First, let's set x as \( 0.\overline{2123} \)

This means that \(10000x=2123.\overline{2123}\)

 

Doing subtracting x from 10000x, we have

 \(10000x-x= 2123.\overline{2123}-0.\overline{2123}\\ 9999x=2123 x=2123/9999\\ x=193/909\)

 

So our final answer is \(\frac{192}{909}\)

 

Thanks! :)

 Jun 13, 2024

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