Percent|Definition & Meaning

Per means each, and cent means hundred, so it shows an amount for each hundred. The symbol used to represent percent is “%”. As the percent is a ratio of two similar types of numbers, it has no scientific dimensions called dimensionless numbers. 

The percent can also be expressed in decimal or fraction form, such as 0.9%, and 0.12%. When it comes to academics, the grades obtained in any subject are calculated in terms of percent. For example, Alina achieved 80% marks in his final exams. This percent is calculated as the sum of Alina’s total marks in all subjects to the total marks.

Formula To Calculate the Percent

The percent is calculated by dividing the given value by the total value and multiplying the result by 100.

Percent = (given value/total value) × 100

For example, Aslam has 10 chocolates. Out of these, he gave 5 chocolates to his brother. Calculate the percentage of the remaining chocolates.

Percentage = 5 / 10 × 100 = 50%

So, the percent of remaining chocolates = 50%

What Is the Formula for Calculating the Percent of a Number

Percent (%) of Number = X

In this case, X represents the percent required.

When the % sign is removed, the above formula can be expressed as follows

P/100 x Number = X

For example, calculate 40% of 50. Let:

40% of 50 = X

40/100×50 = X

X = 20

Percent Difference

It is a measure of the change in a quantity’s value over time expressed in percent. There are some situations in which we need to know if some quantity has increased or decreased as a percent, which is also known as a percent change in the quantity. For example, an increase in poverty, and a decrease in forests.

The Formula for Calculating Percent Differences

The formula below can be used if two values are given and you want to find the percent difference between them.

Percent difference = (x-y) / ({x+y} / 2) × 100

For example, if 50 and 60 are two different values, the percent difference between 50 and 60 can be found by

Percent difference between 50 and 60= (50-60) / ({50+60} / 2) × 100

Increases and Decreases in Percents

Two cases may arise when calculating percent differences, the percent either increases or decreases. A percent increase is calculated by subtracting the original number from the new number, dividing the result by the original number, and multiplying the result by 100. Let us suppose the new number=V₁, whereas the original number is equal to=V₂ then the percent increase can be calculated by using the formula mentioned below:

Percent (%) increase = [(V₁ – V₂) / V₂] × 100

So, increase in number= V₁-V₂ (where V₁ and V₂ represent the new number and the original number)

Accordingly, a percent decrease can also be calculated by subtracting the original number from the new number, dividing the new number by the original number, and multiplying the result by 100. Let us suppose the new number=V₁, whereas the original number is equal to = V₂, then the percent decrease can be calculated by using the formula mentioned below:

Percent (%) decrease = [(V₂ – V₁) / V₂] × 100

So, decrease in number= V₂ – V₁ where V₁ and V₂ represent the original and new number). Therefore, if the answer is negative, then there is a decrease in the percentage of the answer.

How To Convert Fractions to Percents

You can represent a fraction as x/y.

Taking the fraction and multiplying and dividing it by 100, we get the following:

x/y × 100/100 = (x/y × 100) × 1/100……(i)

According to the definition of percent, we can say that 1/100 = 1 percent (%). Equation (i) can therefore be written as follows:

(x/y) × 100%

Hence, by multiplying a fraction by 100, it is possible to convert it to a percent.

There is an interrelationship between fractions, ratios, percent, and decimals. To better understand how to convert one form into another, let’s look at the following table.

Marks Percent

In exams, students are given marks out of 100. In calculating the marks, the percent is used. In the case of a student who scored out of total marks, then the scored marks are to be divided by the total marks and multiplied by 100.

Figure 2 – Formula for calculating the Percentage of obtained marks

Here are a few examples.

Percentage vs. Percent

There is a close relationship between percentage and percent.

Solved Examples for Finding the Percentage

Example 1

If 10% of 50% of a number is 10, then what is the number?

Solution

Suppose the required number is X. As we know that:

10%=10/100 and 50% = 50/100

(10/100) × (50/100) × X = 10

(10×100×100)/ (50×10)

100,000/500

X = 200

Example 2

a. 1/4 is what percent of2/15?

Solution

Suppose X% of 1/4 is 2/15:

(1/4×100) × X = 2/15

X (2/15) × 4 × 100

53%

b. Find out the number which is 20% less than 60.

Solution

Let the required number = X, then:

X = 20% of 60

20/100×60

20×60/100

 X = 12

Example 3

What is the value of the sum of (14%) of 4.2, and (12%) of 4.2)?

Solution

Let the unknown value = X:

X = 14% 4.2+ 12% 4.2

(4.2×14)/100 + ( 4.2×12)/100

0.588 + 0.504

1.092

Example 4: Real-life Problem

In a grocery shop, a shopkeeper has some bananas. He sells 60% bananas and still has 120 bananas. How many bananas did he originally have?

Figure 3 – Bananas in a Shop

Solution

Suppose X = number of bananas he had originally. Based on the question given, we have:

(100-60)% of X = 120

40/100 of X = 120

X = 120 × 100 / 40 = 300

All the mathematical images are generated using GeoGebra.