Extra Questions For Class 9 Maths Chapter 1 | Q4

Number System | Express a recurring infinite decimal as a fraction

Question 4: Express 0.4323232... in the form of \\frac{p}{q}) where p and q are integers and q ≠ 0.


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Explanatory Answer | Chapter 1 Extra Question 4

Let x = 0.4323232…
1000x = 432.3232...
10x = 4.323232...

Why 1000x and 10x?

The objective is to arrive at an integer after the two numbers. The recurring part in 'x' is 0.3232... By multiplying 'x' with a 1000 and a 10, we ensure that the decimal parts in both 1000x and 10x are 0.3232...

Your choice of what to multiply 'x' with will always be determined by the digits that repeat in the decimal component.

1000x – 10x = 432.3232... - (4.323232...)
990x = 428
x = \\frac{428}{990}) = \\frac{214}{495})

 


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