Question

Without actual division, show that each of the following rational number is a terminating decimal. Express in decimal form: \(\dfrac{23}{\left(2^{3} \times 5^{2}\right)}\).

Answer 1

Clearly either 2 or 5 is not factor of 23 , so given fraction is in its simplest form.
Also, the given fraction already in the form of \(\left(2^{\mathrm{m}} \times 5^{\mathrm{n}}\right)\).
Hence, the given rational is a terminating decimal.
We can written it as:
\(\dfrac{23}{\left(2^{3} \times 5^{2}\right)}=\dfrac{23}{200}=0.115\), which is the decimal form.