What Are Percentages?
How "out of 100" became the most useful way to compare numbers in everyday life.
What Does "Percent" Mean?
The word percent comes from the Latin phrase "per centum," which means "for every hundred." A percentage is simply a way of expressing a number as a fraction of 100. When you say "75%," you're saying "75 out of every 100." When a store advertises "20% off," they mean the price is reduced by 20 for every 100 units of currency.
Percentages are everywhere: test scores, weather forecasts, sports statistics, nutrition labels, sales taxes, and battery levels on your phone. They're popular because they give everyone a common scale (out of 100) to compare things that might otherwise be hard to compare.
The Connection: Fractions, Decimals, and Percents
Fractions, decimals, and percentages are three different ways to write the same value. Understanding how to convert between them is one of the most practical math skills you'll ever learn.
Fraction to percent: divide the top number by the bottom, then multiply by 100. For example, 3/4 = 0.75 × 100 = 75%. Decimal to percent: multiply by 100 (or just move the decimal point two places right). 0.45 = 45%. Percent to decimal: divide by 100 (or move the decimal two places left). 60% = 0.60.
Finding a Percentage of a Number
This is the type of percent problem you'll use most often. "What is 25% of 80?" To solve it, convert the percent to a decimal (25% = 0.25) and multiply: 0.25 × 80 = 20. That's it — 25% of 80 is 20.
Here's a real-world example: a $60 video game is on sale for 15% off. What's the discount? 0.15 × 60 = $9 off. So the sale price is $60 − $9 = $51.
Finding What Percent One Number Is of Another
Sometimes you need to work backward: "You scored 18 out of 24 on a quiz — what percent is that?" Divide the part by the whole, then multiply by 100: 18 ÷ 24 = 0.75 × 100 = 75%.
Percent Increase and Decrease
Percentages are also used to describe how much something changes. If a town's population grew from 10,000 to 12,000, the percent increase is: (12,000 − 10,000) ÷ 10,000 × 100 = 20% increase. The formula is: (new − original) ÷ original × 100. The same formula works for decrease — you'll just get a negative number (or subtract the smaller from the larger).
Handy Benchmarks to Memorize
Knowing a few key conversions by heart makes percent problems much faster. 50% = 1/2 (half), 25% = 1/4 (quarter), 10% = 1/10 (just move the decimal one place left), 1% = 1/100 (move the decimal two places left), and 33.3% ≈ 1/3 (one third). Once you know 10%, you can find 5% (half of 10%), 20% (double 10%), and 15% (10% + 5%) quickly in your head.
A "percent" and a "percentage point" are NOT the same thing. If an interest rate goes from 5% to 7%, it increased by 2 percentage points — but the percent increase is actually 40% (because 2 is 40% of 5). This distinction shows up in news about economics and politics all the time, and mixing them up is one of the most common errors in data reporting.
Last reviewed: April 2026