Percentage – Definition, Formulas, and Complete Explanation

What is Percentage?

The word percentage comes from the Latin word “per centum”, which means per hundred.
A percentage is a way of expressing a number as a fraction of 100.

👉 The symbol used for percentage is %

Simple Definition

Percentage means how many parts out of 100.

Example

• 50% means 50 out of 100
• 25% means 25 out of 100
• 100% means 100 out of 100 (the whole)

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Basic Percentage Formula

1. Percentage Formula

$$\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100$$Percentage=(WholePart​)×100

Example

If a student scores 45 marks out of 60:$$\text{Percentage} = \left(\frac{45}{60}\right) \times 100 = 75\%$$Percentage=(6045​)×100=75%

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Converting Fraction to Percentage

$$\text{Fraction} \times 100$$Fraction×100

Examples

• $\frac{1}{2} = 50\%$21​=50%
• $\frac{3}{4} = 75\%$43​=75%
• $\frac{1}{5} = 20\%$51​=20%

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Converting Decimal to Percentage

$$\text{Decimal} \times 100$$Decimal×100

Examples

• 0.25 = 25%
• 0.6 = 60%
• 1.2 = 120%

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Converting Percentage to Fraction

$$\text{Percentage} = \frac{\text{Given value}}{100}$$Percentage=100Given value​

Examples

• 50% = $\frac{50}{100} = \frac{1}{2}$10050​=21​
• 20% = $\frac{20}{100} = \frac{1}{5}$10020​=51​

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Finding Percentage of a Number

Formula

$$\text{Required value} = \frac{\text{Percentage}}{100} \times \text{Number}$$Required value=100Percentage​×Number

Example

Find 20% of 150:$$\frac{20}{100} \times 150 = 30$$10020​×150=30

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Increase in Percentage

Formula

$$\text{Increase \%} = \left(\frac{\text{Increase}}{\text{Original Value}}\right) \times 100$$Increase %=(Original ValueIncrease​)×100

Example

Price increases from 200 to 240:

Increase = 240 − 200 = 40$$\text{Increase \%} = \frac{40}{200} \times 100 = 20\%$$Increase %=20040​×100=20%

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Decrease in Percentage

Formula

$$\text{Decrease \%} = \left(\frac{\text{Decrease}}{\text{Original Value}}\right) \times 100$$Decrease %=(Original ValueDecrease​)×100

Example

Price decreases from 500 to 400:

Decrease = 100$$\text{Decrease \%} = \frac{100}{500} \times 100 = 20\%$$Decrease %=500100​×100=20%

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Percentage Change Formula

$$\text{Percentage Change} = \left(\frac{\text{New Value − Old Value}}{\text{Old Value}}\right) \times 100$$Percentage Change=(Old ValueNew Value − Old Value​)×100

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Important Percentage Values to Remember

Percentage	Fraction	Decimal
10%	1/10	0.1
25%	1/4	0.25
50%	1/2	0.5
75%	3/4	0.75
100%	1	1

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Applications of Percentage

Percentage is widely used in daily life and competitive exams:

• 📘 School exams & results
• 💰 Profit and loss
• 📉 Discounts
• 🧾 GST and tax calculations
• 📊 Statistics
• 🏦 Banking and finance
• 🧠 Competitive exams (SSC, Banking, Police, CTET, PSTET, etc.)

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Percentage in Competitive Exams

Percentage questions are commonly asked in:

• SSC
• Banking exams
• Punjab Government Exams
• CTET / PSTET
• Police and Defence Exams