Percent to Fraction Calculator
Convert percentages to simplified fractions, mixed numbers, and decimals with step-by-step Euclidean GCD reduction.
Conversion Result
How to Convert Percentages to Fractions
A percentage represents a ratio out of 100. Converting any percent into its simplest fraction involves three core mathematical steps:
For deeper analysis and related planning, you can also explore our Area Calculator and Average Calculator.
- Create the Base Fraction: Remove the percent sign and place the value over 100: $\frac{\text{Percent}}{100}$.
- Eliminate Decimals: If the percent contains decimal places, multiply both the numerator and denominator by $10^d$, where $d$ is the number of decimal digits (e.g., $12.5\% \rightarrow \frac{12.5 \times 10}{100 \times 10} = \frac{125}{1000}$).
- Find the Greatest Common Divisor (GCD): Use the Euclidean algorithm to find the greatest common divisor between numerator and denominator. Divide both terms by this GCD to obtain the simplest irreducible fraction.
Common Percent to Fraction Conversion Reference
| Percentage (%) | Fraction (Simplest) | Decimal | Notes |
|---|---|---|---|
| 10% | 1/10 | 0.1 | One tenth |
| 12.5% | 1/8 | 0.125 | One eighth |
| 20% | 1/5 | 0.2 | One fifth |
| 25% | 1/4 | 0.25 | One quarter |
| 33.33% | 1/3 | 0.3333... | One third (repeating) |
| 37.5% | 3/8 | 0.375 | Three eighths |
| 50% | 1/2 | 0.5 | One half |
| 62.5% | 5/8 | 0.625 | Five eighths |
| 66.67% | 2/3 | 0.6667... | Two thirds (repeating) |
| 75% | 3/4 | 0.75 | Three quarters |
| 87.5% | 7/8 | 0.875 | Seven eighths |
| 100% | 1/1 = 1 | 1.0 | Full whole unit |
| 125% | 5/4 = 1 1/4 | 1.25 | Improper fraction / mixed number |
Frequently Asked Questions
How do you convert a percentage into a simplified fraction?
Write the percentage as a fraction with 100 as the denominator (e.g. 75% = 75/100). If the percentage has decimal digits, multiply both the numerator and denominator by 10 for each decimal place to make both numbers integers (e.g. 37.5% = 375/1000). Then find the Greatest Common Divisor (GCD) of both numbers and divide both numerator and denominator by the GCD to achieve the simplest form (e.g. 375/1000 ÷ 125/125 = 3/8).
How do you handle percentages greater than 100%?
Percentages greater than 100% yield improper fractions where the numerator exceeds the denominator (e.g. 175% = 175/100 = 7/4). This can also be expressed as a mixed number by dividing the numerator by the denominator: 7 ÷ 4 = 1 with a remainder of 3, resulting in 1 3/4.
How do you convert a fraction back to a percentage?
Divide the numerator by the denominator to obtain the decimal value, then multiply by 100 and append the percentage symbol (%). For example, 5/8 = 0.625 × 100 = 62.5%.
How do you convert a decimal percentage like 0.75%?
0.75% means $0.75 / 100$. Multiply both numerator and denominator by 100 to eliminate the decimal point: $\frac{75}{10000}$. Find $\gcd(75, 10000) = 25$. Divide both numerator and denominator by 25 to get $\frac{3}{400}$. In decimal form, it equals $0.0075$.
What is the difference between an improper fraction and a mixed number?
An improper fraction has a numerator greater than or equal to its denominator (e.g. $11/4$). A mixed number separates the whole integer portion from the proper fractional remainder: $11/4 = 2\frac{3}{4}$ ($11 \div 4 = 2$ with a remainder of 3).
Can a percentage be negative?
Yes. Negative percentages represent drops or losses (e.g., $-25\%$). In fraction form, the negative sign is retained in front of the fraction or on the numerator: $-\frac{1}{4}$.