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# 1. Percentage

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100, which means, a part per hundred. The word per cent means per 100. It represented by the symbol “%”. Percentages have no dimension, hence are dimensionless numbers. If we say, 50% of a number, then it means 50 per cent of its whole. Also, learn how to calculate percentage here.

Percentages can also be represented in decimal or fraction form, such as 0.6%, 0.25%, etc. In academics, the marks obtained in any subject are calculated in terms of percentage. Like, Ram has got 78% of marks in his final exam. So, this percentage is calculated on account of total marks obtained by Ram in all subjects to the total marks.

• Formula
• Percentage of a number
• Example
• Fraction to percentage
• Percentage vs Per cent
• Percentage in Maths
• Tricks
• Solved problems

## Percentage Formula

To determine the percentage, we have to divide the numerator by denominator and then multiply the resultant to 100.

Percentage formula = (Numerator/Denominator)×100

Example: 2/5 × 100 = 0.4 × 100 = 40 per cent

### How to calculate percentage of a number?

To calculate the percentage of a number, we need to use a different formula such as:

P% of Number = X

where X is the required percentage.

If we remove the % sign, then we need to express the above formulas as;

P/100 * Number = X

Example: Calculate 10% of 80.

Let 10% of 80 = X

10/100 * 80 = X

X = 8

## Percentage Example

Two quantities are generally expressed on the basis of their ratios. Here, let us understand the concepts of percentage through a few examples in a much better way.

## Converting Fractions to Percentage

A fraction can be represented by ab.

Multiplying and dividing the fraction by 100, we have

ab×100100 = (ab×100)1100 ………………(i)

From the definition of percentage, we have =1100 = 1%

Thus equation (i) can be written as: =ab×100%

Thus fraction can be converted to percentage simply by multiplying the given fraction by 100.

## Difference between Percentage and Percent

The word percentage and percent are related closely to each other.

Percent ( or symbol %) is accompanied with a specific number.

Eg: More than 75% of the participants responded with their positive response to abjure.

Percentage is represented without a number, is used generally for general case of percent.

Eg: The percentage of the population affected by malaria is between 60% and 65%.

Fractions, Ratios, Percents and Decimals are interrelated with each other. Let us look on to the conversion of one form to other:

## Percentage in Math’s

Every percent problem has three possible unknowns, or variables :

• The percent
• The part
• The base

In order to solve any per cent problem, you must be able to identify these variables.

Look at the following examples. All three variables are known:

Example : 70% of 30 is 21

• 70 is the percent.
• 30 is the base.
• 21 is the part.

Example : 25% of 200 is 50

• 25 is the percent.
• 200 is the base.
• 50 is the part.

Example : 6 is 50% of 12

• 6 is the part.
• 50 is the percent.
• 12 is the base.

## Percentage Tricks

To calculate the percentage we can use the given below tricks.