Question

Find after how many places of decimal the decimal form of the number $\frac{27}{2^3.5^4.3^2}$ will terminate.

Answer 1

$$\begin{gathered} \frac{27}{2^3.5^4.3^2}=\frac{3^3}{2^3.5^4.3^2} \\ =\frac{3}{2^3.5^4} \\ =\frac{3}{8\times 625} \\ =\frac{3}{5000} \\ =\frac{0.003}{5} \\ =0.0006 \end{gathered}$$

Hence, after four places of decimal the decimal form of the number $\frac{27}{2^3.5^4.3^2}$ will terminate.