Decimal to Fraction Calculator
Convert any decimal to a fraction with step-by-step solutions and simplification
Convert Decimal to Fraction
Enter any decimal number
Example Conversions
Terminating Decimal
Example: 0.125
Steps:
1. Count decimal places: 3
2. Denominator = 10³ = 1000
3. Numerator = 125
4. Fraction = 125/1000
5. GCD(125, 1000) = 125
Result: 125/1000 = 1/8
Repeating Decimal
Example: 0.333... = 0.(3)
Steps:
1. Let x = 0.333...
2. 10x = 3.333...
3. 10x - x = 3.333... - 0.333...
4. 9x = 3
Result: x = 3/9 = 1/3
Conversion Methods
Terminating Decimals
Count decimal places
Use powers of 10 as denominator
Repeating Decimals
Use algebraic method
Multiply and subtract to eliminate repetition
Simplification
Find GCD of numerator and denominator
Divide both by their greatest common divisor
Quick Tips
Every terminating decimal can be written as a fraction
0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4
For repeating decimals, use the algebraic method
Always simplify your final fraction
Understanding Decimal to Fraction Conversion
What Is Decimal to Fraction Conversion?
Converting a decimal to a fraction means expressing a decimal number as a ratio of two integers (a numerator and a denominator). This conversion helps in exact representations and mathematical operations where precision is crucial.
Why Convert Decimals to Fractions?
- •Exact representation without rounding errors
- •Easier to work with in mathematical operations
- •Better for understanding proportions and ratios
- •Essential for many real-world applications
Conversion Methods
Terminating Decimals
For decimals that end:
1. Count decimal places (n)
2. Denominator = 10ⁿ
3. Numerator = decimal × 10ⁿ
Example: 0.125 → 125/1000 → 1/8
Repeating Decimals
For decimals with repeating patterns:
1. Let x = repeating decimal
2. Multiply by 10ⁿ (n = repeat length)
3. Subtract original equation
Example: 0.333... → x = 1/3