Question

Express p/q form of 10.03636......

Answer 1

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= $\frac{9936/18}{990/18}$ ( Divide both top and bottom to reduce)

x = $\frac{552}{55}$

So, 10.03636...... can be represent as 552/55.