Question

What is the mean proportional between the number 0.32 and 0.02?
(a) 0.08
(b) 0.04
(c) 0.06
(d) 0.64

Answer 1

Hint: The mean proportional is the geometric mean. The geometric mean or the mean proportional is defined as the square root of the product of the given two numbers. The formula to calculate the mean proportional of two numbers $a$ and $b$ is given as $\sqrt{a\times b}$. We will use this formula to find the mean proportional of the given two numbers.

Complete step-by-step answer:
The given two numbers are 0.32 and 0.02. We know that the mean proportional is the geometric mean, which is defined as the square root of the product of the given two numbers. That means, for two numbers $a$ and $b$, we know that the mean proportional is given as $\sqrt{a\times b}$. We will use this definition to calculate the mean proportional for 0.32 and 0.02 as follows,
$\text{mean proportional = }\sqrt{0.32\times 0.02}$
We will solve the above equation by multiplying the two numbers and then taking the square root. We get the following,
$\begin{align}
  & \text{mean proportional = }\sqrt{0.0064} \\
 & =0.08
\end{align}$
Hence, the mean proportional of 0.32 and 0.02 is 0.08.

So, the correct answer is “Option (a)”.

Note: The geometric mean of two numbers $a$ and $b$is also called as the mean proportional because it can be expressed as the means of a proportion. That is, if $x$ is the mean proportional of the two numbers $a$ and $b$, then it represents the three numbers to be proportional in the following way: $\dfrac{a}{x}=\dfrac{x}{b}$. When we simplify this ratio, we get the formula of the geometric mean, which is $x=\sqrt{a\times b}$.