Question

What percent of 80 is 8 ?

Answer 1

Hint: To calculate the percentage of any quantity, we need to first understand the meaning of the term ‘percent’. Percent means to calculate a quantity per one hundred parts. To calculate what percentage of 80 is 8, we will first derive the decimal form and then multiply it with hundred. This will give us the answer to our problem.

Complete step by step solution:
In order to find what percent of 80 is 8, we will first convert 8 into its decimal form. Let this decimal form number be termed as ‘x’. Then, ‘x’ can be calculated as follows:
$\begin{align}
  & \Rightarrow x=\dfrac{8}{80} \\
 & \Rightarrow x=\dfrac{1}{10} \\
 & \therefore x=0.1 \\
\end{align}$
Let us name the above equation as$(1)$, so we have:
$\Rightarrow x=0.1$ ......... (1)

Now, we need to find the percentage of ‘x’ when its decimal value is known. We know that any decimal can be converted into its percentage by multiplying it with one hundred. So, we proceed in our solution in the following manner:
Let the percentage of ‘x’ be given by ‘y’. Then, we can write that:
$\Rightarrow y=\left( x\times 100 \right)\%$
Putting the value of ‘x’ from equation number (1) in the above equation, we get:

$\begin{align}
  & \Rightarrow y=\left( 0.1\times 100 \right)\% \\
 & \therefore y=10\% \\
\end{align}$
Thus, we get the final percentage as 10%.
Hence, we can say that 10% of 80 is 8.

Note: Whenever, we calculate the percentage of any quantity, that is, of a fraction or a decimal, it is always a non-negative term. Another interesting property of percentage is that the terms in it can be reversed, that is, x% of y is equal to y% of x. For example: 5% of 100 is equal to 5 and 100% of 5 is also equal to 5. It can be used to get faster solutions to problems with percentage calculation in it.