Question
Without actual division, show that the following rational numbers is a terminating decimal. Express in decimal form:$\frac{19}{3125}$
✓
Answer
$\frac{19}{3125}=\frac{19}{5^5}=\frac{19\times2^5}{5^5\times2^5}$$=\frac{608}{100000}=0.00608$
We know either $2$ or $5$ is not a factor of $19$, 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 $19$, 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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