Question
Without actual division, show that the following rational numbers is a terminating decimal. Express in decimal form:$\frac{171}{800}$
✓
Answer
$\frac{171}{800}=\frac{171}{2^5\times5^2}=\frac{171\times5^3}{2^5\times5^5}$$=\frac{21375}{100000}=0.21375$
We know either $2$ or $5$ is not a factor of $171$, so it is in its simplest form.
Moreover, it is in the form of $(2^m\times 5^n)$.
Hence, the given rational is terminating.
We know either $2$ or $5$ is not a factor of $171$, so it is in its simplest form.
Moreover, it is in the form of $(2^m\times 5^n)$.
Hence, the given rational is terminating.
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