Show that 0.2636363… can be expressed in the form p/q, where p and q are integers and q≠0, what is the value of p/q ?

Correct option is C

Given
Number = 0.2636363...

Solution
Let x = 0.263636....(Equation 1)
Multiply both sides by 10 to place the repeating part immediately after the decimal point:
10x = 2.636363....(.Equation 2)
Multiply Equation 2 by 100 (because 2 digits repeat):
1000x = 263.636363.... (Equation 3)
Subtract Equation 2 from Equation 3:
​$$1000x - 10x = 263.636363\dots - 2.636363\dots \\\ \\990x = 261 \\x = \frac{261}{990}$$​​
Simplify the fraction by dividing the numerator and denominator by 9:
​$$x = \frac{29}{110}$$​​

Final Answer
So the correct answer is (c)