Question

when the repeating decimal 0.363636...... is written in simplest fractional form p/q, find the sum p+q

Answer 1

given that
x = 0.363636.......    ----(1)
period  = 36
periodicity = 2
so 
100 x =36.363636......   -------(2)
from (1) and (2)
100 x = 36.363636.....
       x =    0.363636......     (-)
_____________________  
99 x = 36
      x =36/99
      x = 4/11
p/q = 4/11

then p = 4  ; q = 11
p+q = 4+11
        = 15.