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Conversion Terminating and Non-Terminating Recurring Decimals to P/Q Form

Represent 0.5...

Question

Represent 0.555555… in a rational form. What is the smallest natural number by which you should multiply the obtained fraction, so that it becomes a terminating decimal. [ 4 MARKS]

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Solution

Concept : 2 Marks
Calculation : 2 Marks

Let x = 0.5555 ...(equation 1)

Hence 10x = 5.5555555 ...(equation 2)

So , 9x=5 (On subtracting equation 1 from equation 2)

$x = \frac{5}{9}$

The obtained fraction is $\frac{5}{9}$ . If we multiply the given fraction by 9 (the smallest possible natural number), the fraction will change to 5. Hence terminating.

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