Question

change in two p/q form 15.7121212...

Answer 1

15.7121212... is nothing but  15.712  ( i am giving the bar symbol on down of the no.s it is 12 bar)

let,  x = 15.712 = 15.7121212... -----------------1
then 1000x = 15712.12 = 15712.121212... ------------2
        10x = 157.12 = 157.1212.. ----------- 3

subtract equation 3 with 2
so,
        1000x = 15712.1212....
            10x = 00157.1212....
         -           -
       ------------------------------------
          990x = 15555.0000...
       ------------------------------------
              x = 15555/990
              x = 3111/198

therefore the fractional form (p/q) of 15.7121212... is 3111/198
      

Answer 2

let x be the term in p/q form
15.712.........................
10x=157.12...........................
1000x=15712.12........................................
1000x-10x=(15712.12...................)-(157.12.........)
990x=15555
x=15555/990
x=3111/198