Without actually performing the long division,

Question:

Without actually performing the long division, find if $\frac{987}{10500}$ will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer.

Solution:

Yes, after simplification denominator has factor 53 -22 and which is of the type 2m . 5″. So, this is terminating decimal.

$\because \quad \frac{987}{10500}=\frac{47}{500}=\frac{47}{5^{3} \cdot 2^{2}} \times \frac{2}{2}$

$=\frac{94}{5^{3} \times 2^{3}}=\frac{94}{(10)^{3}}=\frac{94}{1000}=0.094$

 

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