Question

convert the following rational numbers into decimal without actual division 75/12​

Answer 1

6.25

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Answer 2

$Given \: Rational \:number \: \frac{75}{12}$

$Least \: form \: of \: given \: rational \: number \\ = \frac{ 3 \times 25}{3 \times 4} \\= \frac{25}{4}\\= \frac{25}{2^{2}}\\= \frac{ 25 \times 5^{2}}{2^{2} \times 5^{2}}\\= \frac{25 \times 25}{(2\times 5)^{2}}\\= \frac{625}{10^{2}} \\= \frac{625}{100} \\= 6.25\:\blue{ ( Terminating \:decimal )}$

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

Therefore.,

$\red{ \frac{75}{12} } \green { = 6.25}$

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