Percentage to Fraction Converter
Convert any percentage to a simplified fraction — enter your percentage value below.
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How to Convert a Percentage to a Fraction
Since "percent" means "per hundred," every percentage is already a fraction with denominator 100. The process is:
- Write the percentage over 100: n% = n/100
- Simplify by dividing both by their GCD.
n% = n / 100 → simplify by dividing by GCD(n, 100)
Worked Examples
Example 1: Convert 60%
- 60% = 60/100
- GCD(60, 100) = 20
- 60/100 = 3/5
Example 2: Convert 37.5% (decimal percentage)
- 37.5% = 37.5/100
- Multiply both by 2 to clear the decimal: 75/200
- GCD(75, 200) = 25
- 75/200 = 3/8
Example 3: Convert 120% (over 100%)
- 120% = 120/100
- GCD(120, 100) = 20
- 120/100 = 6/5 = 1 1/5 (mixed number)
Common Percentage to Fraction Reference
| Percentage | Fraction | Percentage | Fraction |
|---|---|---|---|
| 10% | 1/10 | 60% | 3/5 |
| 20% | 1/5 | 66.67% | 2/3 |
| 25% | 1/4 | 75% | 3/4 |
| 33.33% | 1/3 | 80% | 4/5 |
| 50% | 1/2 | 90% | 9/10 |
Real-World Applications
- Taxes: A 25% tax rate = 1/4 of income.
- Sales: A 30% discount means you pay 70% = 7/10 of the price.
- Statistics: A 40% success rate = 2/5 of trials succeeded.
- Nutrition: A food providing 12.5% of daily calcium = 1/8 of daily needs.
Common Mistakes to Avoid
- Forgetting to simplify: 40% = 40/100, but the final answer should be 2/5, not 40/100.
- Decimal percentages: Clear the decimal before finding the GCD. Multiply both numerator and denominator by the appropriate power of 10.
Frequently Asked Questions
How do you convert a percentage to a fraction?
Write the percentage over 100, then simplify. For example, 75% = 75/100 = 3/4 (GCD = 25).
What is 50% as a fraction?
50% = 50/100 = 1/2. Divide both by GCD(50,100) = 50.
How do you convert a percentage greater than 100% to a fraction?
Same method: 150% = 150/100 = 3/2 (an improper fraction = 1 1/2 as a mixed number).
How do you convert a repeating percentage like 33.33...% to a fraction?
33.333...% = 1/3 exactly, because 1/3 × 100 = 33.333... This is a known exact conversion.
Is the Percentage to Fraction converter free?
Yes, completely free. No registration, no limits, no hidden fees.