The Percentage Concept – What Does Percent Mean?
A percentage is simply a way of expressing a number as a part of 100. The word itself comes from the Latin phrase per centum, meaning "by the hundred." Once you understand what a percentage represents, every other percentage topic — discounts, interest, profit, and more — becomes straightforward.
What Does Percent Mean?
Percent means out of 100. So 47% means 47 out of every 100, or 47/100. The % symbol is just a shorthand for "out of 100."
Visualising Percentages
Imagine a square divided into 100 equal small squares. If you shade 30 of them, you have shaded 30% of the square. That is 30/100 = 0.30 = 30%.
The Three Forms of the Same Value
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
| 1/100 | 0.01 | 1% |
Converting Between Forms
| From | To Percentage | Example |
|---|---|---|
| Fraction | Divide top by bottom, then times 100 | 3/4 times 100 = 75% |
| Decimal | Multiply by 100 | 0.6 times 100 = 60% |
| Percentage | Divide by 100 | 45% = 45/100 = 0.45 |
Percentages Greater Than 100%
Percentages are not limited to 0-100. A value can be 150% if it is one-and-a-half times its reference amount. A business growing by 200% means it is now three times its original size.
Real-Life Uses of Percentages
- A shop offers 20% off a jacket.
- A bank pays 3.5% interest per year on savings.
- A student scores 84% on a test.
- A mobile phone battery is at 62%.
- The population of a city grew by 5% this year.
An Important Note on 100%
100% always means the whole thing — the complete amount. 50% is always half of whatever amount you are working with. The reference amount can change, so 50% of 200 is not the same as 50% of 500.
Key Takeaways
- Percent means out of 100. The symbol % means /100.
- Fractions, decimals, and percentages are three faces of the same value.
- To convert a fraction or decimal to a percentage, multiply by 100.
- To convert a percentage back, divide by 100.
- Percentages can exceed 100% when a value is more than the whole reference amount.
Practice Questions
- Write 3/5 as a percentage.
- Write 0.07 as a percentage.
- Write 85% as a decimal and as a fraction.
- A jar has 100 sweets. 37 are red. What percentage is red?
- What percentage of 1 hour is 15 minutes?