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What is the product of the numerator and the denominator when $0.\overline{09}$ is expressed as a fraction in lowest terms?

 Dec 14, 2021
edited by wiseowl  Dec 14, 2021
edited by wiseowl  Dec 14, 2021
 #2
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0.0909090909 ...

 

100*0.0909090909 ... = 9.09090909 ...

1 *0.0909090909 ...    = 0.0909090909 ...

subract

99*0.0909090909 ...=9

0.0909090909 ...=9/99 = 1/11

 Dec 15, 2021

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