Question
Without actual division, show that the following rational numbers is a terminating decimal. Express in decimal form:$\frac{15}{1600}$
✓
Answer
$\frac{15}{1600}=\frac{15}{2^6\times5^2}=\frac{15\times5^4}{2^6\times5^6}$$=\frac{9375}{1000000}=0.009375$
We know either 2 or 5 is not a factor of 15, 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 15, 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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