Let's assume x= 10.03636........ (1)
Multiply each sides by 100. So,
100x = 1003.63636.......... (2)
Next step is to subtract the equation (1) and (2)
100x - x= 1003.63636- 10.03636
99x= 993.6
99x*10 = 993.6 (By multiplying each sides by 10 to get rid of decimal)
990x = 9936
990x/990 = 9936/990 ( Divide each sides by 990)
x= [tex] \frac{9936/18}{990/18} [/tex] ( Divide both top and bottom to reduce)
x = [tex] \frac{552}{55} [/tex]
So, 10.03636...... can be represent as 552/55.
