Question

Express the rational number 15.71212121212.... in p/q form

Answer 1

let X=15.71212.... 1equation
multiplying both sides by 100
100X=71.21212.... 2equation

subtracting 1equa. from 2equa.

Answer 2

Let
15.7 121212.......=x
Then 100x=1571.212121.........
{why should we multiply with 100 only?
Ans:-because two numbers (i.e.,1,2)are repeating}
Now let
X=15.7121212.......be equation 1
100x=1571.212121.......be equation 2
Subtract equation 1 from equation 2
100x=1571.21212121.....
- x=15.7121212......
-------------------------------
99x=1555.5
{212121.....will cancel from both the equations}
X=1555.5/99
X=15555/990