Question

express 5.4178 [bar on 178] in the p/q form

Answer 1

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 .               

Answer 2

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........