The decimal expansion of the rational number nbsp-3322 -160- -215- -160-5 nbsp-will terminate after nbsp-a- one decimal place nbsp- nbsp- nbsp- nbsp- -b- nbsp- Two decimal places nbsp-c- three decimal places nbsp- nbsp- -d- more than 3 decimal places nbsp-

Consider the rational number3322 #215;5. Denominator of the above rational number is of the form 2m #215;2n, so the rational number has terminating decimal ...

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Standard IX

Mathematics

Decimal Expansion of Rational and Irrational Numbers

The decimal e...

Question

The decimal expansion of the rational number $\frac{33}{2^{2} \times 5}$ will terminate after
(a) one decimal place (b) Two decimal places
(c) three decimal places (d) more than 3 decimal places

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Solution

Consider the rational number $\frac{33}{2^{2} \times 5}$ .
Denominator of the above rational number is of the form $2^{m} \times 2^{n}$ , so the rational number has terminating decimal expansion.
$\frac{33}{2^{2} \times 5} = \frac{33 \times 5}{2^{2} \times 5^{2}} = \frac{165}{100} = 1.65$
So, the decimal expansion of the given rational number terminates after two decimal places.

Hence, the correct answer is option B.

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The decimal expansion of the rational number 3322 × 5 will terminate after (a) one decimal place (b) Two decimal places (c) three decimal places (d) more than 3 decimal places

The decimal expansion of the rational number $\frac{33}{2^{2} \times 5}$ will terminate after
(a) one decimal place (b) Two decimal places
(c) three decimal places (d) more than 3 decimal places