# Extra Questions For Class 9 Maths Number Systems | Q3

###### NCERT Class 9 Chapter 1 | Express a recurring infinite decimal as a fraction

Question 3: Express 1.363636... in the form $\frac{p}{q}$, where p and q are integers and q ≠ 0.

## NCERT Solution to Class 10 Maths

### Explanatory Answer | Number System Extra Question 3

Let x = 1.363636...
Thus, 100x = 136.3636...

#### Why 100x?

The objective is to arrive at an integer after subtracting the decimal component. The decimal part in x is 0.3636.... If we multiply 100 to x, the decimal part of 100x is also 0.3636...

Your choice of what to multiply x with will always be determined by the decimal component.

100x – x = 136.3636... - 1.363636...
99x = 135
x = $\frac{135}{99}$ = $\frac{15}{11}$

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