What Is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning "per hundred." Percentages are everywhere — from sale discounts and tax rates to nutrition labels and exam scores.
The symbol % means "out of 100." So 45% means 45 out of every 100, or 45/100, which equals 0.45 as a decimal.
Converting Between Percentages, Decimals, and Fractions
| Percentage | Decimal | Fraction |
|---|---|---|
| 25% | 0.25 | 1/4 |
| 50% | 0.50 | 1/2 |
| 75% | 0.75 | 3/4 |
| 10% | 0.10 | 1/10 |
| 1% | 0.01 | 1/100 |
To convert a percentage to a decimal, divide by 100 (or move the decimal point two places left). To go from decimal to percentage, multiply by 100.
Finding a Percentage of a Number
Multiply the number by the percentage as a decimal.
Example: What is 30% of 250?
250 × 0.30 = 75
Calculating What Percentage One Number Is of Another
Divide the part by the whole, then multiply by 100.
Example: 18 out of 24 students passed. What percentage passed?
(18 ÷ 24) × 100 = 0.75 × 100 = 75%
Percentage Increase and Decrease
These are essential for understanding price changes, growth, and comparisons.
% Change = ((New Value − Old Value) ÷ Old Value) × 100
Example: A jacket was $80, now $60. What's the percentage decrease?
((60 − 80) ÷ 80) × 100 = (−20 ÷ 80) × 100 = −25% (a 25% decrease)
Real-World Applications of Percentages
- Shopping discounts: A 20% off sale on a $150 item saves you $30.
- Tax calculations: If sales tax is 8%, a $50 item costs $54 in total.
- Interest rates: A 5% annual interest rate on a $1,000 loan adds $50 per year.
- Nutrition labels: "15% of your daily intake" tells you how much of a nutrient one serving provides.
- Grades: Scoring 36 out of 40 on a test = 90%.
- Tips: A 15% tip on a $60 restaurant bill = $9.
Mental Math Shortcuts for Percentages
- 10%: Move the decimal one place to the left. (10% of 340 = 34)
- 5%: Find 10%, then halve it. (5% of 340 = 17)
- 1%: Move the decimal two places to the left. (1% of 340 = 3.4)
- 15%: Find 10% + 5%. (15% of 340 = 34 + 17 = 51)
- 25%: Divide by 4. (25% of 340 = 85)
Key Takeaway
Percentages are one of the most universally useful math skills you can develop. Whether you're comparing prices, reading data, or calculating a tip, the ability to work fluently with percentages gives you a meaningful advantage in everyday decision-making.