Understanding Percentages

What You’ll Learn

In this lesson you’ll learn what a percentage is, how it connects to fractions and decimals, and how to read and write percentages in everyday situations.

The Concept

Percentage means “per hundred.” The % symbol stands for /100.

Examples:

• $25\% = \frac{25}{100} = 0.25$
• $100\% = \frac{100}{100} = 1$ (the whole)
• $50\% = \frac{50}{100} = \frac{1}{2} = 0.5$
• $150\% = \frac{150}{100} = 1.5$ (more than the whole)

To think of it: 20% of 100 dollars is 20 dollars, or 20 per hundred dollars.

Percentages can be more than 100% (growth) or less than 1% (very small parts).

Worked Examples

Convert these to decimals and fractions:

1. $75\% = \frac{75}{100} = 0.75 = \frac{3}{4}$
2. $8\% = \frac{8}{100} = 0.08 = \frac{2}{25}$
3. $200\% = \frac{200}{100} = 2.00 = 2$ (whole + same amount again)

Real-World Applications

Percentages are used for discounts (20% off a 50-dollar shirt = 10 dollars off), tips (15% of 40 dollars bill = 6 dollars tip), tax (8% sales tax on 120 dollars = 9.60 dollars), or interest rates. Understanding “percent” as “out of 100” makes these everyday calculations easier to grasp.

You’ve Got This

Percent just means “out of 100.” Think of it as a special fraction with 100 on the bottom. Practice by converting sale signs or tips in your head (20% of 100 dollars is 20 dollars). It becomes second nature fast.

Quiz

What does 40% mean?

• A.40 per 100
• B.40 per 1000
• C.4 per 100
• D.40 per 10

Convert 75% to a decimal.

• A.0.75
• B.7.5
• C.0.075
• D.75.0

A salary increase of 5% means what?

• A.5 dollars more per 100 dollars
• B.50 dollars more per 100 dollars
• C.5 per 1000
• D.5 times more

What is 150% of a number?

• A.1.5 times the number
• B.15 times the number
• C.0.15 times the number
• D.150 times the number

Express 0.08 as a percent.

• A.8%
• B.0.8%
• C.80%
• D.0.08%