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Express \( 0.\overline{1}+0.\overline{01}+0.\overline{0001}\)  as a common fraction.

 Aug 5, 2019
 #1
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    x = 0.111111.....                 y = 0.01010101......                  z = 0.0001000100010001.....

10x = 1.11111.....             100y = 1.01010101.....         10000z = 1.000100010001.....

  9x = 1                              99y = 1                                9999z = 1

   x = 1/9                                y = 1/99                                   z = 1/9999

 

   x+y+z = 1213/9999

 Aug 5, 2019

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