Question

check whether 14588/625 a terminating decimal expansion if yes write its decimal expansion ​

Answer 1

$Given \: Rational \: number \: \frac{14588}{625}$

$= \frac{14588}{5\times 5 \times 5 \times 5 } \\= \frac{14588}{5^{4}} \: \green{ ( Terminating \:decimal)}$

$\blue{ Since \: denominator \: is \: in \:the }\\\blue{ form \: of \: 2^{n} 5^{m} . }$

Decimal Expansion:

$\red{\frac{14588}{625} }\\= \frac{14588}{5^{4}}\\= \frac{14588\times 2^{4}}{2^{4} \times 5^{4}}\\= \frac{14588\times 16}{(2 \times 5)^{4}}\\= \frac{233408}{10^{4}} \\= \frac{233408}{10000} \\= 23.3408$

Therefore.,

$\red{\frac{14588}{625}} \green { = 23.3408}$

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