Question

How do you find the difference between two numbers as a percentage?

Answer 1

Hint:In this question, we need to explain how to find the difference between two numbers as a percentage. Percentage is nothing but it is a number or a ratio expressed in the fraction of \[100\] . First, we need to know that concept and formula for the difference between two numbers as a percentage that is a percentage difference. Then we can explain the difference between two numbers as a percentage with an example.

Complete step by step solution:
First we can know what the percentage difference is.
The percentage difference of any two numbers is nothing but the absolute value of the ratio of their difference and their average multiplied by \[100\] .
Percentage difference formula :
Percentage difference is equal to the absolute value of the change in value, divided by the average of the two numbers and all multiplied by \[100\] .
\[\Rightarrow \ \text{Percentage difference} = \dfrac{\left| V_{1} – V_{2} \right|}{(\dfrac{V_{1} + V_{2}}{2})} \times 100\]
With this formula, we can find the percentage difference of any two numbers.
Now let us consider an example to find the percentage difference.
What is the percentage difference between \[5\] and \[7\] ?
Here we need to find the percentage difference between \[5\] and \[7\] .
Let us consider \[V_{1} = 5\] and \[V_{2} = 7\]
Then we know that,
\[\text{Percentage difference} = \dfrac{\left| V_{1} – V_{2} \right|}{(\dfrac{V_{1} + V_{2}}{2})} \times 100\]
Now on substituting the values pf \[V_{1}\] and \[V_{2}\] in the formula,
We get,
\[\Rightarrow \dfrac{\left| 5 – 7 \right|}{(\dfrac{5 + 7}{2})} \times 100\]
On simplifying,
We get,
\[\Rightarrow \dfrac{\left| - 2 \right|}{(\dfrac{12}{2})} \times 100\]
On further simplifying,
We get,
\[\Rightarrow \dfrac{2}{6} \times 100\]
On dividing,
We get,
\[\Rightarrow \ 0.333 \times 100\]
By multiplying,
We get,
\[\Rightarrow \ 33.3\%\]
Thus the percentage difference of \[5\] and \[7\] is \[33.3\%\]
We need to know that if we consider \[V_{1} = 7\] and \[V_{2} = 5\] also we get the same percentage difference because we are calculating a difference between two numbers and not a change from one number to another.
In order to find the percentage difference of any two numbers, find the absolute value of the ratio of their difference and their average and multiply that value by \[100\].

Note:
We may get confused with percentage difference and the percentage change. The percentage difference is used to understand the percentage of the difference when compared to the average between two numbers whereas the Percentage change is to identify the percentage between the two numbers. The percentage difference is an important calculation used in comparing the two similar numbers when the direction and relationship context between them is unavailable.