Number system practice

Express non terminating decimal as fraction

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

Video Explanation

Explanatory Answer

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})