Percentage to Decimal Calculator: Convert Fractions, Decimals & Percentages
A percentage to decimal calculator converts between three fundamental number representations: percentages (parts per hundred), decimals (base-10 fractions), and fractions (ratios of integers), enabling seamless transformation by dividing percentages by 100 to get decimals, multiplying decimals by 100 for percentages, and converting fractions through division then scaling. This calculator simplifies mathematical operations, grade calculations, financial computations, statistical analysis, probability problems, and everyday percentage tasks by providing instant conversions with step-by-step formulas for students learning number systems, professionals calculating discounts and interest rates, data analysts working with proportions, and anyone needing to switch between percentage, decimal, and fraction formats for accurate calculations and clear communication.
🔢 Interactive Conversion Calculator
Convert between percentages, decimals, and fractions
Percentage to Decimal Converter
Convert percentage to decimal by dividing by 100
Decimal to Percentage Converter
Convert decimal to percentage by multiplying by 100
Fraction to Decimal and Percentage
Convert fraction to both decimal and percentage
Understanding Number Conversions
Percentages, decimals, and fractions are three ways to represent the same values. Understanding how to convert between them is essential for mathematics, finance, science, and everyday calculations.
Conversion Formulas
Percentage to Decimal
Formula:
\[ \text{Decimal} = \frac{\text{Percentage}}{100} \]
Examples:
75% = 75 ÷ 100 = 0.75
50% = 50 ÷ 100 = 0.50
12.5% = 12.5 ÷ 100 = 0.125
Decimal to Percentage
Formula:
\[ \text{Percentage} = \text{Decimal} \times 100 \]
Examples:
0.75 = 0.75 × 100 = 75%
0.50 = 0.50 × 100 = 50%
0.125 = 0.125 × 100 = 12.5%
Fraction to Decimal and Percentage
Fraction to Decimal:
\[ \text{Decimal} = \frac{\text{Numerator}}{\text{Denominator}} \]
Decimal to Percentage:
\[ \text{Percentage} = \frac{\text{Numerator}}{\text{Denominator}} \times 100 \]
Example: \( \frac{3}{4} = 0.75 = 75\% \)
Complete Conversion Reference Table
| Fraction | Decimal | Percentage |
|---|---|---|
| \( \frac{1}{2} \) | 0.5 | 50% |
| \( \frac{1}{3} \) | 0.333... | 33.33% |
| \( \frac{1}{4} \) | 0.25 | 25% |
| \( \frac{1}{5} \) | 0.2 | 20% |
| \( \frac{1}{8} \) | 0.125 | 12.5% |
| \( \frac{1}{10} \) | 0.1 | 10% |
| \( \frac{2}{3} \) | 0.666... | 66.67% |
| \( \frac{3}{4} \) | 0.75 | 75% |
| \( \frac{4}{5} \) | 0.8 | 80% |
| \( \frac{3}{8} \) | 0.375 | 37.5% |
| \( \frac{5}{8} \) | 0.625 | 62.5% |
| \( \frac{7}{8} \) | 0.875 | 87.5% |
Common Percentage Conversions
| Percentage | Decimal | Percentage | Decimal |
|---|---|---|---|
| 1% | 0.01 | 60% | 0.60 |
| 5% | 0.05 | 70% | 0.70 |
| 10% | 0.10 | 75% | 0.75 |
| 15% | 0.15 | 80% | 0.80 |
| 20% | 0.20 | 85% | 0.85 |
| 25% | 0.25 | 90% | 0.90 |
| 30% | 0.30 | 95% | 0.95 |
| 40% | 0.40 | 100% | 1.00 |
| 50% | 0.50 | 150% | 1.50 |
Step-by-Step Examples
Example 1: Converting Percentage to Decimal
Problem: Convert 65% to a decimal
Step 1: Write the percentage
65%
Step 2: Divide by 100
65 ÷ 100 = 0.65
Alternative method: Move decimal point 2 places left
65. → 0.65
Answer: 65% = 0.65
Example 2: Converting Decimal to Percentage
Problem: Convert 0.85 to a percentage
Step 1: Write the decimal
0.85
Step 2: Multiply by 100
0.85 × 100 = 85
Step 3: Add percent symbol
85%
Alternative method: Move decimal point 2 places right
0.85 → 85.
Answer: 0.85 = 85%
Example 3: Converting Fraction to Decimal and Percentage
Problem: Convert \( \frac{3}{8} \) to decimal and percentage
Step 1: Divide numerator by denominator
3 ÷ 8 = 0.375
Decimal answer: 0.375
Step 2: Multiply decimal by 100 for percentage
0.375 × 100 = 37.5%
Percentage answer: 37.5%
Summary: \( \frac{3}{8} = 0.375 = 37.5\% \)
Quick Conversion Methods
Moving Decimal Points
Shortcut Techniques:
Percentage to Decimal: Move decimal 2 places LEFT
- • 45% → 45. → 0.45
- • 8% → 08. → 0.08
- • 125% → 125. → 1.25
Decimal to Percentage: Move decimal 2 places RIGHT
- • 0.45 → 45. → 45%
- • 0.08 → 08. → 8%
- • 1.25 → 125. → 125%
Real-World Applications
Academic Use
- Grade calculation: 85% = 0.85 for GPA calculations
- Test scores: Convert fractions to percentages (18/20 = 90%)
- Probability: Express chances as decimals or percentages
- Statistics: Report data in most appropriate format
Financial Applications
- Interest rates: 5% APR = 0.05 for calculations
- Discounts: 25% off = multiply by 0.75
- Tax calculations: 7% sales tax = 0.07
- Investment returns: Express gains as percentages
- Loan payments: Convert APR to decimal for formulas
Everyday Use
- Tips: 20% tip = multiply bill by 0.20
- Sales: 30% off means pay 70% (0.70)
- Recipes: Scale ingredients using decimals
- Sports statistics: Batting averages, completion rates
Special Cases
Percentages Over 100%
Values Greater Than 1:
150% = 150 ÷ 100 = 1.50
200% = 200 ÷ 100 = 2.00
350% = 350 ÷ 100 = 3.50
These represent values greater than the whole (more than 100%)
Percentages Less Than 1%
Small Percentages:
0.5% = 0.5 ÷ 100 = 0.005
0.25% = 0.25 ÷ 100 = 0.0025
0.1% = 0.1 ÷ 100 = 0.001
Common in interest rates, error margins, quality control
Repeating Decimals
Common Repeating Patterns
| Fraction | Decimal (exact) | Decimal (rounded) | Percentage |
|---|---|---|---|
| \( \frac{1}{3} \) | 0.333... | 0.33 | 33.33% |
| \( \frac{2}{3} \) | 0.666... | 0.67 | 66.67% |
| \( \frac{1}{6} \) | 0.1666... | 0.17 | 16.67% |
| \( \frac{5}{6} \) | 0.8333... | 0.83 | 83.33% |
| \( \frac{1}{7} \) | 0.142857... | 0.14 | 14.29% |
Common Mistakes to Avoid
⚠️ Frequent Errors
- Wrong direction: 50% ≠ 50 (it equals 0.50)
- Forgetting to divide/multiply by 100: Essential step
- Decimal point errors: 5% = 0.05, not 0.5
- Percentage over 100: 150% = 1.5, not 15
- Fraction division: Divide numerator by denominator, not reverse
- Rounding too early: Keep extra decimals until final answer
- Symbol confusion: Remember to add % or drop it appropriately
Conversion Tips and Tricks
Quick Mental Math:
- 50% = half = 0.5
- 25% = quarter = 0.25
- 75% = three quarters = 0.75
- 10% = one tenth = 0.1
- 1% = one hundredth = 0.01
- Double a percentage: Multiply decimal by 2
- Half a percentage: Divide decimal by 2
- Remember: Percent means "per hundred"
Frequently Asked Questions
How do you convert percentage to decimal?
Divide the percentage by 100 or move the decimal point two places to the left. Example: 65% ÷ 100 = 0.65. Quick method: 65% → 65. → 0.65. This works because percent means "per hundred," so you're finding how many out of 100. Always remove the % symbol when converting to decimal format.
How do you convert decimal to percentage?
Multiply the decimal by 100 or move the decimal point two places to the right, then add %. Example: 0.65 × 100 = 65%. Quick method: 0.65 → 65. → 65%. This reverses the percentage-to-decimal conversion. Any decimal can become a percentage, including values over 1.00 (which become percentages over 100%).
How do you convert a fraction to decimal and percentage?
Divide the numerator by denominator to get decimal, then multiply by 100 for percentage. Example: 3/4 → 3 ÷ 4 = 0.75 → 0.75 × 100 = 75%. One calculation gives both forms. For repeating decimals (like 1/3 = 0.333...), round to desired precision (usually 2 decimal places or 33.33%).
Why do we divide by 100 to convert percentage to decimal?
Because "percent" literally means "per hundred" (from Latin per centum). 50% means 50 per 100, which equals 50/100 = 0.50. The % symbol represents division by 100. Converting reverses this: multiplying by 100 adds the "per hundred" back. Understanding this etymology helps remember the conversion direction and mathematical reasoning behind it.
What is 0.5 as a percentage?
0.5 = 50%. Calculate: 0.5 × 100 = 50%. Or move decimal two places right: 0.5 → 50. → 50%. This represents half (1/2) or 50 out of 100. Common equivalent: 0.5 = 1/2 = 50%. Memorizing common conversions (0.5 = 50%, 0.25 = 25%, 0.75 = 75%) speeds up calculations.
Can percentages be over 100%?
Yes, percentages can exceed 100%, representing values greater than the whole. Example: 150% = 1.50 (one and a half times). Common in growth rates, sales increases, or comparisons. 200% means double. When converting to decimal, same rule applies: divide by 100. So 250% = 2.50. Percentages can also be negative, representing decreases or losses.
Key Takeaways
Converting between percentages, decimals, and fractions requires understanding that these are three representations of the same values. The key is dividing or multiplying by 100 to move between percentages and decimals, and performing fraction division to get decimal form.
Essential principles to remember:
- Percentage to decimal: Divide by 100 (or move decimal 2 left)
- Decimal to percentage: Multiply by 100 (or move decimal 2 right)
- Fraction to decimal: Divide numerator by denominator
- Fraction to percentage: Divide then multiply by 100
- Percent means "per hundred" (out of 100)
- 50% = 0.5 = 1/2 (all equivalent)
- Percentages can exceed 100% (values over 1.0)
- Always add/remove % symbol appropriately
- Keep extra decimal places until final answer
- Use conversions for calculations, percentages for communication
Getting Started: Use the interactive calculator at the top of this page to convert between percentages, decimals, and fractions instantly. Select your conversion type, enter your value, and receive immediate results with step-by-step explanations. Perfect for homework, work calculations, or everyday percentage problems.