Question

45/1200 is a terminating decimal say true or false, explain

Answer 1

Answer:

And it's decimal expansion is 0.0375

Answer 2

$Given \: rational \: number = \frac{45}{1200} \\= \frac{ 3 \times 3 \times 5 }{ 3 \times 2^{4} \times 5^{2} } \\= \frac{ 3}{2^{4} \times 5 } \\= \frac{ 3\times 5^{3}}{2^{4} \times 5 \times 5^{3} } \\= \frac{ 3\times 125}{2^{4} \times 5^{4} } \\= \frac{ 375}{(2\times 5)^{4} } \\= \frac{ 375}{10^{4} } \\= \frac{375}{10000} \\= 0.0375 \: \blue { ( Terminating \: Decimal )}$

Therefore.,

$\red { \frac{45}{1200} } \green { = 0.0375}\\ \blue { ( Terminating \: Decimal )}$

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