Decimal to Fraction Calculator
Convert decimals to fractions
Decimal to Fraction Calculator
Convert decimal numbers to fractions and mixed numbers
For repeating decimals like 0.333... (enter 1), or 0.363636... (enter 2)
For 0.333... enter 1
About Converting Decimals to Fractions
Converting decimals to fractions is a fundamental math skill that helps you work with numbers in different forms.
Every decimal can be expressed as a fraction. Terminating decimals (like 0.75) convert easily, while repeating decimals (like 0.333...) require a special algebraic method.
Understanding this conversion helps with cooking measurements, construction work, and mathematical calculations.
Types of Decimals
• Terminating: Decimals that end (0.75, 2.625)
• Repeating: Decimals with repeating patterns (0.333..., 0.142857...)
• Non-repeating: Irrational numbers (π, √2)
How to Convert Decimals to Fractions
For Terminating Decimals
- Write the decimal divided by 1 - Place the decimal over 1
- Multiply to remove decimal point - Multiply both top and bottom by 10, 100, 1000, etc.
- Find the GCD - Find the greatest common divisor of numerator and denominator
- Simplify the fraction - Divide both by the GCD
- Convert to mixed number if needed - If improper, convert to mixed number
For Repeating Decimals
- Let x equal the decimal - x = 0.333...
- Multiply by power of 10 - 10x = 3.333...
- Subtract the equations - 10x - x = 3.333... - 0.333...
- Solve for x - 9x = 3, so x = 3/9 = 1/3
Example 1: 0.75
Step 1: 0.75/1
Step 2: (0.75 × 100)/(1 × 100) = 75/100
Step 3: GCD(75, 100) = 25
Step 4: 75÷25 / 100÷25 = 3/4
Result: 3/4
Example 2: 2.625
Step 1: 2.625/1
Step 2: 2625/1000
Step 3: GCD(2625, 1000) = 125
Step 4: 2625÷125 / 1000÷125 = 21/8
Step 5: 21/8 = 2 5/8
Result: 2 5/8
Common Decimal to Fraction Conversions
Decimal | Fraction | Type |
---|---|---|
0.5 | 1/2 | Terminating |
0.25 | 1/4 | Terminating |
0.75 | 3/4 | Terminating |
0.333... | 1/3 | Repeating |
0.666... | 2/3 | Repeating |
0.125 | 1/8 | Terminating |
0.2 | 1/5 | Terminating |
0.1666... | 1/6 | Repeating |
Real-World Applications
Cooking & Recipes
Convert decimal measurements to fractions for easier measuring with cups and spoons (e.g., 0.375 cups = 3/8 cup).
Construction & Carpentry
Convert decimal inch measurements to fractional inches for precise cuts and measurements (e.g., 2.625" = 2 5/8").
Finance & Accounting
Express decimal percentages as fractions for easier calculations and understanding of proportions.
Tips for Success
Remember These Patterns:
- • 0.1 = 1/10, 0.01 = 1/100, 0.001 = 1/1000
- • Count decimal places to find denominator power of 10
- • Always simplify to lowest terms
- • Repeating decimals often have 3, 6, 9, or 11 in denominator
Common Mistakes to Avoid:
- • Forgetting to simplify the fraction
- • Not recognizing repeating patterns
- • Miscounting decimal places
- • Confusing terminating with repeating decimals