Question
Without actual division, show that the following rational numbers is a terminating decimal. Express in decimal form:$\frac{24}{125}$
✓
Answer
$\frac{24}{125}=\frac{24}{5^3}=\frac{24\times2^3}{5^3\times2^3}$$=\frac{192}{1000}=0.192$
We know $5$ is not a factor of $24,$ 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 $5$ is not a factor of $24,$ 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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