Write the decimal expansion of

Question:

Write the decimal expansion of $\frac{73}{\left(2^{4} \times 5^{3}\right)}$.

 

Solution:

Decimal expansion:

$\frac{73}{\left(2^{4} \times 5^{3}\right)}=\frac{73 \times 5}{2^{4} \times 5^{4}}$

$=\frac{365}{(2 \times 5)^{4}}$

$=\frac{365}{(10)^{4}}$

$=\frac{365}{10000}$

$=0.0365$

Thus, the decimal expansion of $\frac{73}{\left(2^{4} \times 5^{3}\right)}$ is $0.0365$.

 

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