The repeating digits are 16, our number is going to be called x, x= 0.161616. If we multiply x by 100 we have, 16.1616. So we are going to formulate the following equation
100*x - x = 16.1616.. - 0.1616...
After subtracting x from 100 x , w have
99x = 16
Dividing by 99 on both sides of the equation
x = 16/99
Answer is 16/99, because it can not be simplyfied.