Question

What type of decimal form will the no 24/125 show? Give reasons.

Answer 1

$Given \: rational \: number \: \frac{24}{125}$

$Here, \:denominator \: 125 = 5^{3}\: is \:of \:the \\form \\2^{n} \times 5^{m} ,\: n = 0 \:and \:m = 3$

$So, \frac{24}{125} \: is \: a \: terminating \\decimal$

$\underline {\green{ Explanation : }}$

$\frac{24}{125} \\= \frac{24}{5^{3}} \\= \frac{24\times 2^{3}}{2^{3} \times 5^{3}} \\=\frac{24\times 8}{10^{3}} \\=\frac{192}{1000}\\= 0.192 \\ \pink {( terminating \:decimal)}$

Therefore.,

$\red{\frac{24}{125}}\green {= 0.192 }$

$\pink {(terminating \:decimal)}$

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Answer 2

Answer:

the no. 24/125 is a terminating