The product of two numbers is 0.008 and one is $\frac{1}{5}$ of the other. Find the numbers.
Answer
Answer (as printed):
Explanation
Let the numbers be $x$ and $\frac{x}{5}$. Then, $$x \times \frac{x}{5}=0.008 \Rightarrow \frac{x^{2}}{5}=0.008 \Rightarrow x^{2}=0.008 \times 5=0.04 \Rightarrow x=\sqrt{0.04}=0.2 .$$ $$\therefore \text { Greater number }=0.2 . \text { Smaller number }=\frac{0.2}{5}=0.04 .$$ Hence, the required numbers are 0.2 and 0.04.
Explanation as extracted from the printed page; notation may be imperfect.