Percentages and Conversions (Introduction)
Understand why percent means "per hundred" and master the conversions between fractions, decimals, and percentages.
Percentages are everywhere: sales discounts, tax rates, interest, tips, test scores, raises. If you can't convert between %, decimals, and fractions — you're guessing at your own finances. Mastering this gives you real control over money decisions.
- Define percent as "parts per hundred" and connect it to fractions and decimals
- Convert fluently between fractions, decimals, and percentages
- Calculate a percentage of a number in real-world scenarios
Percent literally means "per hundred." So 50% = \(\frac{50}{100}\) = 0.5. All three forms represent the exact same value — they're just different ways to write it.
\[ 50\% = \frac{50}{100} = \frac{1}{2} = 0.5 \]The key shortcuts: % → decimal: divide by 100 (move dot 2 places left). Decimal → %: multiply by 100 (move dot 2 places right).
The Conversion Table
Fraction ↔ Decimal ↔ Percent — Quick Reference
| Fraction | Decimal | Percent | Common Use |
|---|---|---|---|
| \(\frac{1}{4}\) | 0.25 | 25% | Quarter price off |
| \(\frac{1}{2}\) | 0.5 | 50% | Half price |
| \(\frac{3}{4}\) | 0.75 | 75% | Three-quarter discount |
| \(\frac{1}{10}\) | 0.1 | 10% | Quick tip estimate |
| \(\frac{1}{5}\) | 0.2 | 20% | Standard restaurant tip |
Write 35% as a decimal and as a fraction.
- Decimal: \(35\% \div 100 = 0.35\)
- Fraction: \(\frac{35}{100} = \frac{7}{20}\) (divide by 5)
What is 10% of $80?
Shortcut: 10% = 0.10. To find 10% of any number, just move the decimal one place left.
\[ 10\% \text{ of } 80 = 0.10 \times 80 = \$8 \]Then 20% = double that = $16. And 5% = half of 10% = $4. Build from 10%!
A jacket costs $120 and is 25% off. What do you pay?
- Find the discount: \(25\% \text{ of } 120 = 0.25 \times 120 = \$30\)
- Subtract from original: \(120 - 30 = \$90\)
Or use the shortcut: you're paying 75% of the price → \(0.75 \times 120 = \mathbf{\$90}\).
Try these:
- Convert 0.08 to a percentage.
- What is 15% of $60?
- A TV marked $450 is 20% off. What's the sale price?
▶ Show Answers
- 8% — 0.08 × 100 = 8.
- $9 — 10% of $60 = $6; half of that = $3; $6+$3 = $9. Or: 0.15 × 60 = 9.
- $360 — 20% of 450 = 90; 450 − 90 = 360. Or: 0.80 × 450 = 360.
- Forgetting to divide by 100: 25% is not 25 — it's 0.25. Multiply by 25 instead of 0.25 and you get a number 100× too large.
- "Percent of" vs "percent off": "15% of $80" = $12 (the amount). "15% off $80" = $80 − $12 = $68 (the price you pay). These are different steps.
- Calculating the discount but forgetting to subtract: You found the savings — now subtract it from the original price to get what you actually owe.
- Percent = per hundred — 45% = 45/100 = 0.45.
- % → decimal: divide by 100 (or move dot 2 left).
- Decimal → %: multiply by 100 (or move dot 2 right).
- "X% of Y" = (X/100) × Y — convert to decimal first, then multiply.
Sales professionals calculate commission as a percentage of revenue. Financial advisors express returns, fees, and rates as percentages. Tax preparers calculate income tax as a percentage of taxable income. Almost every financial conversation you'll have professionally involves converting and applying percentages.
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Percentages and Conversions (Introduction) — Quiz
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