Question

show that 1.272727 ... = 1.27 can be expressed in the form p/q ,where p and q are integers and q # 0.please explain clearly.

Answer 1

x=1.272727.............(1)
      multiply both sides by 100
100x=100*1.2727.......
100x=127.2727.....
100x=126+1.272727......
100x=126+x   [from (1)]
100x-x=126
99x=126
    x=126/99=42/33
                   =14/11
    

Answer 2

Let x = 1.272727...........
Because two digits are repeating, we multiply x by 100
     100x = 12.272727...........
So, 100x = 126 + 1.272727... = 126 + x
   ∴ 100x - x = 126
    = 99x = 126
So x = 126/99
        = 14/11
So x = 14/11