Introduction
Imagine you go shopping and see a 50% discount on your favorite toy. But what does 50% mean? The word percentage comes from “per cent,” meaning “per hundred.” It helps us compare values, calculate marks, understand discounts, and even analyze statistics! Percentage is everywhere – in finance, sports, business, and daily life.
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Where Does Percentage Come From?
The concept of percentages dates back to ancient Rome, where merchants used fractions to calculate taxes. Over time, mathematicians developed the decimal system, and percentage became a common way to express parts of a whole. Today, percentages are used worldwide in business, banking, and education.
What Is Percentage?
A percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol “%”.
- Example: 50% means 50 out of 100 or 50/100 = 1/2.
- Example: If a student scores 80% in an exam, it means they got 80 marks out of 100.
Converting Fractions, Decimals, and Ratios to Percentage
| Type | Example | Convert to % |
| Fraction | 1/4 | (1 ÷ 4) × 100 = 25% |
| Decimal | 0.75 | 0.75 × 100 = 75% |
| Ratio | 2:5 | (2 ÷ 5) × 100 = 40% |
Why Do We Need Percentage?
- Comparing Values: Helps compare marks, profits, and losses easily.
- Finance & Banking: Used in interest rates, taxes, and loans.
- Shopping & Discounts: Helps calculate price reductions.
- Statistics & Data Analysis: Used in surveys and reports.
- Health & Fitness: Used in body fat percentage, calorie intake, etc.
How Is Percentage Helpful?
- Education: Used to calculate exam results and attendance.
- Business: Companies use it to measure profits and losses.
- Sports: Athletes use percentages to track their performance.
- Science: Used in chemistry (solutions) and biology (population growth).
- Cooking: Used in food nutrition and recipe adjustments.
Fundamentals of Percentage & Important Formulas
- Finding Percentage of a Number:
- Percentage=(PartTotal)×100\text{Percentage} = \left( \frac{\text{Part}}{\text{Total}} \right) × 100Percentage=(TotalPart)×100
- Converting Percentage to Decimal:
- Decimal=Percentage100\text{Decimal} = \frac{\text{Percentage}}{100}Decimal=100Percentage
- Finding Percentage Increase or Decrease:
- Percentage Change=(New Value−Old ValueOld Value)×100\text{Percentage Change} = \left( \frac{\text{New Value} – \text{Old Value}}{\text{Old Value}} \right) × 100Percentage Change=(Old ValueNew Value−Old Value)×100
5 Basic & 5 Problem-Solving Questions
Basic Questions
- Convert 0.45 into a percentage.
- Find 25% of 200.
- Express 3/5 as a percentage.
- If a student scored 80 out of 100, what is the percentage?
- Convert 75% into a fraction and a decimal.
Problem-Solving Questions
- A T-shirt costs ₹800, and there is a 20% discount. Find the final price.
Solution: Discount = (20/100) × 800 = ₹160
Final Price = ₹800 – ₹160 = ₹640 - A shopkeeper earns a 15% profit on a ₹5000 item. Find the profit amount.
Solution: Profit = (15/100) × 5000 = ₹750 - If a student got 75 marks out of 150, find their percentage.
Solution:- (75/150)×100=50(75/150) × 100 = 50%(75/150)×100=50
- The population of a city increased from 20,000 to 25,000. Find the percentage increase.
Solution:- 25000−2000020000×100=25\frac{25000 – 20000}{20000} × 100 = 25%2000025000−20000×100=25
- A water tank is 40% full. If the tank’s total capacity is 500 liters, find the amount of water in the tank.
Solution:- (40/100)×500=200 liters(40/100) × 500 = 200 \text{ liters}(40/100)×500=200 liters
Real-Life Examples & Fun Facts
- Blood Composition: Human blood is 55% plasma and 45% cells.
- Earth’s Water: 71% of the Earth’s surface is covered with water.
- Cloud Coverage: Meteorologists use percentage to measure how much of the sky is cloudy.
- Sports Records: Athletes’ performance is analyzed in percentage.
- Exam Results: Many schools grade students using percentage-based scores.
Outcomes & Fun Facts
- Percentage helps in everyday decisions, from shopping to fitness tracking.
- It is widely used in banking, finance, and statistics.
- Even nature follows percentages – forests cover about 31% of Earth’s land!
- The first use of percentage signs (%) appeared in the 15th century.
Conclusion
Percentage is a powerful mathematical tool that helps us compare, calculate, and analyze data. Whether you are planning a budget, tracking fitness, or calculating discounts, understanding percentage makes life easier!
Challenge: Can you calculate how much percentage of your day is spent sleeping if you sleep 8 hours out of 24?
