Fractions, Decimals, and Percentages
Fractions, decimals, and percentages are different ways to show the same part of a whole. Learn how to convert between all three forms.
Quick answer
Divide a fraction’s numerator by its denominator to get a decimal. Multiply a decimal by 100 to get a percentage. To turn a percentage into a decimal, divide by 100.
Fraction → decimal: numerator ÷ denominator Decimal → percent: decimal × 100 Percent → decimal: percent ÷ 100Three ways to show the same value
Fractions, decimals, and percentages can represent exactly the same quantity. A fraction shows a ratio, a decimal shows division, and a percentage expresses a value out of 100.
For example, one-half, 0.5, and 50% all mean the same amount.
Common fraction, decimal, and percent conversions
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/10 | 0.1 | 10% |
| 1/8 | 0.125 | 12.5% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333... | 33.333...% |
| 1/2 | 0.5 | 50% |
| 2/3 | 0.666... | 66.666...% |
| 3/4 | 0.75 | 75% |
| 4/5 | 0.8 | 80% |
| 1 | 1.0 | 100% |
Convert a fraction to a decimal
Divide the numerator, which is the top number, by the denominator, which is the bottom number.
Example: Convert 3/4 to a decimal
- Identify the numerator: 3
- Identify the denominator: 4
- Divide: 3 ÷ 4 = 0.75
Answer: 3/4 = 0.75.
Example: Convert 7/20 to a decimal
- Divide the numerator by the denominator: 7 ÷ 20 = 0.35
Answer: 7/20 = 0.35.
Convert a decimal to a percentage
Multiply the decimal by 100, then add the percent symbol. Moving the decimal point two places to the right gives the same result.
Example: Convert 0.72 to a percentage
- Multiply by 100: 0.72 × 100 = 72
- Add the percent sign: 72%
Answer: 0.72 = 72%.
Example: Convert 0.045 to a percentage
- Multiply by 100: 0.045 × 100 = 4.5
- Add the percent sign: 4.5%
Answer: 0.045 = 4.5%.
Convert a percentage to a decimal
Divide the percentage by 100 and remove the percent symbol. Moving the decimal point two places to the left gives the same result.
Example: Convert 18% to a decimal
- Divide by 100: 18 ÷ 100 = 0.18
Answer: 18% = 0.18.
Example: Convert 125% to a decimal
- Divide by 100: 125 ÷ 100 = 1.25
Answer: 125% = 1.25.
Convert a fraction to a percentage
The universal method is to divide the numerator by the denominator, then multiply the decimal by 100. You can also rewrite some fractions with a denominator of 100.
Example: Convert 3/5 to a percentage
- Divide: 3 ÷ 5 = 0.6
- Multiply by 100: 0.6 × 100 = 60
Answer: 3/5 = 60%.
Equivalent-fraction method: Convert 1/4 to a percentage
- Multiply numerator and denominator by 25: 1/4 = 25/100
- Read the numerator as a percentage: 25/100 = 25%
Answer: 1/4 = 25%.
Convert a percentage to a fraction
Write the percentage as a fraction over 100, then simplify the fraction by dividing the numerator and denominator by their greatest common factor.
Example: Convert 45% to a fraction
- Write the percentage over 100: 45% = 45/100
- Divide numerator and denominator by 5: 45/100 = 9/20
Answer: 45% = 9/20.
Example: Convert 12.5% to a fraction
- Write the decimal percentage over 100: 12.5/100
- Remove the decimal by multiplying top and bottom by 10: 125/1000
- Simplify: 125/1000 = 1/8
Answer: 12.5% = 1/8.
Convert a decimal to a fraction
Write the digits after the decimal point over a power of 10, then simplify. The denominator depends on the number of decimal places.
Example: Convert 0.35 to a fraction
- There are two decimal places, so write 35 over 100: 35/100
- Simplify by dividing by 5: 35/100 = 7/20
Answer: 0.35 = 7/20.
Example: Convert 0.625 to a fraction
- There are three decimal places, so write 625/1000
- Simplify by dividing by 125: 625/1000 = 5/8
Answer: 0.625 = 5/8.
Repeating decimals and rounding
Some fractions produce repeating decimals. For example, 1/3 equals 0.333... and 2/3 equals 0.666.... Their percentage forms are 33.333...% and 66.666...%.
When a result repeats, round it only when the situation calls for a limited number of decimal places. In general math work, use an ellipsis to show that the decimal continues or state the rounding precision.
Frequently asked questions
How do you convert a fraction to a percentage?
Divide the numerator by the denominator, then multiply by 100. For example, 3/4 = 0.75, and 0.75 × 100 = 75%.
How do you convert a decimal to a percentage?
Multiply the decimal by 100 and add a percent sign. For example, 0.25 × 100 = 25%, so 0.25 is 25%.
How do you convert 25% to a fraction?
Write 25% as 25/100, then simplify by dividing the numerator and denominator by 25. The result is 1/4.
What is 0.75 as a fraction and percentage?
As a fraction, 0.75 is 75/100, which simplifies to 3/4. As a percentage, 0.75 × 100 = 75%.
Can a percentage be greater than 100%?
Yes. Percentages greater than 100% represent an amount larger than one whole. For example, 125% equals 1.25 or 5/4.