Question
Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non terminating repeating decimal expansion.
$\frac{987}{10500}$
$\frac{987}{10500}$
✓
Answer
The given number is
$\frac{987}{10500}=\frac{987\div21}{10500\div21}=\frac{47}{500}$
Now, $500 = 2^2 \times 5^3$
The denominator can be written in the form of $2^m \times 5^n.$
So, the given number has a terminating decimal expansion.
$\frac{987}{10500}=\frac{47}{500}=\frac{47}{5^3\times2^2}\times\frac{2}{2}$ $\frac{94}{5^3\times2^3}=\frac{94}{1000}=0.094$
$\frac{987}{10500}=\frac{987\div21}{10500\div21}=\frac{47}{500}$
Now, $500 = 2^2 \times 5^3$
The denominator can be written in the form of $2^m \times 5^n.$
So, the given number has a terminating decimal expansion.
$\frac{987}{10500}=\frac{47}{500}=\frac{47}{5^3\times2^2}\times\frac{2}{2}$ $\frac{94}{5^3\times2^3}=\frac{94}{1000}=0.094$
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