Three forms, one value
Fractions, decimals and percents are three ways to write the same value. Being able to convert quickly lets you pick the easiest form for each problem.
| Fraction | Decimal | Percent |
|---|---|---|
| 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% |
| 1/8 | 0.125 | 12.5% |
| 1/3 | 0.333… | 33 1/3% |
| 2/3 | 0.666… | 66 2/3% |
| 1 | 1.0 | 100% |
The conversion map
| From → To | How | Example |
|---|---|---|
| Fraction → decimal | Divide numerator by denominator | 3/8 = 3 ÷ 8 = 0.375 |
| Decimal → percent | Multiply by 100 (move point 2 right) | 0.375 → 37.5% |
| Percent → decimal | Divide by 100 (move point 2 left) | 62% → 0.62 |
| Percent → fraction | Write over 100, simplify | 62% = 62/100 = 31/50 |
| Decimal → fraction | Use place value, simplify | 0.62 = 62/100 = 31/50 |
| Fraction → percent | Make the denominator 100, or convert to a decimal first | 7/20 = 35/100 = 35% |
Why ×100 works
Percent means hundredths. 0.375 is 37.5 hundredths, so it’s 37.5%.
Tricky cases
- Percents with decimals: 12.5% = 0.125 = 125/1,000 = 1/8
- Percents over 100: 140% = 1.4 = 1 2/5
- Percents under 1: 0.4% = 0.004 = 1/250
- Repeating decimals: 1/3 = 0.333… = 33.3…% (often written 33 1/3% or about 33.3%)
Choosing the best form
- To compare, decimals are easiest: is 3/8 or 0.4 bigger? 0.375 < 0.4.
- To calculate a part, fractions can be easiest: 25% of 64 = 1/4 of 64 = 16.
- To communicate, percents are clearest: "38% of voters".
Ordering mixed forms
Example: Order 0.6, 5/8, 58% from least to greatest.
Convert all to decimals: 0.6, 0.625, 0.58 → 58%, 0.6, 5/8.
Worked examples
Example 1: Write 0.07 as a percent.
0.07 × 100 = 7%. (Not 70%!)
Example 2: Write 45% as a fraction in simplest form.
45/100 = 9/20.
Example 3: Write 3/40 as a percent.
3 ÷ 40 = 0.075 → 7.5%.
Common mistakes
- Moving the decimal point the wrong way: 0.35 is 35%, not 0.0035%.
- 0.07 vs 0.7: 0.07 = 7%, 0.7 = 70%.
- Forgetting to simplify fractions.
Try it yourself
- 0.82 as a percent
- 4% as a decimal
- 3/5 as a percent
- 175% as a mixed number
- Order: 1/3, 0.3, 32%
Answers: 1) 82% 2) 0.04 3) 60% 4) 1 3/4 5) 0.3, 32%, 1/3
Quick recap
- Fractions, decimals and percents are equivalent forms.
- Decimal ↔ percent: move the point 2 places.
- Choose the form that makes the task easiest.