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2015-06-07T12:35:59+05:30

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Let x = 5.4178178....-------------(1)
Here periodicity is 3
So,we have to multiply x with 1000
⇒1000×x = 1000×5.4178178...
⇒1000x = 5417.81781781..---------(2)
Now,(2) -(1)= 
                   1000x = 5417.8178178...
                          x =      5.4178178...
             ⇒ 999x = 5412.4000........
             ⇒ x = 54124/9990
Therefore , p/q = 54124/9990 .               

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2015-06-08T16:07:33+05:30

This Is a Certified Answer

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Let x = 5.4178178.....
Here , periodicity is 3 
So, x is to be multiplied by 1000
⇒ x × 1000 = 5.4178178......× 1000
⇒1000x = 5417.8787.......... 
Now,1000x-x = 1000x=5417.8178.....
                              x=0005.4178..........
      ⇒999x = 5412.4000......
      ⇒x = 54124/9990 = 5.4178178........


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