Without actually dividing find-whether 1323-63-352has a terminating or non terminating decimal expansion-

The nbsp;given nbsp;number nbsp;is, nbsp; nbsp; nbsp; nbsp; nbsp;132363 nbsp; #215; nbsp;352=33 nbsp; #215; nbsp;722 #215;33 nbs ...

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Standard IX

Mathematics

Irrational Numbers and Properties of Irrational Numbers

Without actua...

Question

Without actually dividing find,whether 1323/6³*35²has a terminating or non terminating decimal expansion.

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Solution

$The given number is, \frac{1323}{6^{3} \times 35^{2}} = \frac{3^{3} \times 7^{2}}{{(2 \times 3)}^{3} \times {(5 \times 7)}^{2}} = \frac{3^{3} \times 7^{2}}{2^{3} \times 3^{3} \times 5^{2} \times 7^{2}} = \frac{1}{2^{3} \times 5^{2}} Since the denominator of the given number is of the form of 2^{m} 5^{n}, where m and n are non negative integers, so given number has terminating decimal expansion .$

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Without actually dividing find,whether 1323/63*352has a terminating or non terminating decimal expansion.

The given number is, 132363 × 352=33 × 722×33 × 5×72=33 × 7223 × 33 × 52 × 72=123 × 52Since the denominator of the given number is of the form of 2m 5n, where m and n are non negative integers, so given number has terminating decimal expansion.

Without actually dividing find,whether 1323/6³*35²has a terminating or non terminating decimal expansion.