How to Convert a Percentage to a Fraction
Converting a percentage to a fraction involves two simple steps: put the percentage over 100 to create a fraction, then simplify by finding the greatest common divisor (GCD) of the numerator and denominator. Since 'percent' means 'per hundred,' any percentage can be directly written as a fraction with 100 as the denominator.
Steps to Convert Percentage to Fraction
- 175% = 75/100 = 3/4 (divide both by 25)
- 237.5% = 37.5/100 = 375/1000 = 3/8 (multiply by 10, then simplify)
- 3150% = 150/100 = 3/2 = 1 and 1/2 (as mixed number)
Common Percentage to Fraction Conversions
| Percentage | Fraction | Decimal |
|---|---|---|
| 10% | 1/10 | 0.1 |
| 12.5% | 1/8 | 0.125 |
| 20% | 1/5 | 0.2 |
| 25% | 1/4 | 0.25 |
| 33.33% | 1/3 | 0.333 |
| 37.5% | 3/8 | 0.375 |
| 40% | 2/5 | 0.4 |
| 50% | 1/2 | 0.5 |
| 60% | 3/5 | 0.6 |
| 62.5% | 5/8 | 0.625 |
| 66.67% | 2/3 | 0.667 |
| 75% | 3/4 | 0.75 |
| 80% | 4/5 | 0.8 |
| 87.5% | 7/8 | 0.875 |
| 90% | 9/10 | 0.9 |
| 100% | 1/1 | 1.0 |
Converting Decimal Percentages to Fractions
When the percentage has a decimal (like 12.5% or 37.5%), first multiply both numerator and denominator by 10 (or 100) to eliminate the decimal. Then simplify. For example: 12.5% = 12.5/100 = 125/1000 = 1/8. For 6.25%: 6.25/100 = 625/10000 = 1/16.
Percentages greater than 100% convert to improper fractions (numerator larger than denominator) or mixed numbers. For example, 250% = 250/100 = 5/2 = 2 1/2. This represents a value that is 2.5 times the whole.