Without actually performimg the division- find whether- 39625 will have terminating or non terminating decimal expansions- Give reason-

39625 p/q is terminating if p and q are co prime and q is in the form of 2^n5^m 625 = 5^4, #160; and 39 and 625 have no factor ...

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Standard IX

Mathematics

Check If a Given Rational Number Is Terminating or Not

Without actua...

Question

Without actually performimg the division, find whether, $\frac{39}{625}$ will have terminating or non terminating decimal expansions. Give reason.

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Solution

$\frac{39}{625}$
$p/q is terminating if$
$p and q are co - prime$
$and q is in the form of 2^{n} 5^{m}$
$625 = 5^{4},$
$and 39 and 625 have no factor in common$
$∴ Terminating Decimal$

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Without actually performimg the division, find whether,39625 will have terminating or non terminating decimal expansions. Give reason.

39625p/qis terminating if p and q are co - primeand q is in the form of 2n5m625=54, and 39 and 625 have no factor in common∴ Terminating Decimal

Without actually performimg the division, find whether, $\frac{39}{625}$ will have terminating or non terminating decimal expansions. Give reason.

$\frac{39}{625}$
$p/q is terminating if$
$p and q are co - prime$
$and q is in the form of 2^{n} 5^{m}$
$625 = 5^{4},$
$and 39 and 625 have no factor in common$
$∴ Terminating Decimal$