Decimal to Fraction Calculator
Convert Decimals to Fractions
Enter any decimal number to convert it to its simplest fraction form.
Conversion Result
Visual Representation:
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Simplification Steps:
The decimal represents a part of a whole, while the fraction shows the same value as a ratio of two integers.
Common Decimal to Fraction Conversions
What is Decimal to Fraction Conversion?
Converting decimals to fractions is the process of expressing a decimal number (a number with a decimal point) as a fraction (a ratio of two integers). This conversion is useful for better understanding proportions and for mathematical operations that are easier with fractions.
Conversion Methods
1. Place Value Method
Use the place value of the last digit to determine the denominator.
0.75 = 75/100 = 3/4 (after simplification)
2. Multiplication Method
For repeating decimals, use algebraic methods to convert to fractions.
Step-by-Step Conversion Process
Example 1: Convert 0.75 to Fraction
- Write decimal as fraction: 0.75 = 75/100
- Simplify by finding GCD: GCD of 75 and 100 is 25
- Divide numerator and denominator by GCD: 75÷25 = 3, 100÷25 = 4
- Result: 3/4
Example 2: Convert 0.6 to Fraction
- Write decimal as fraction: 0.6 = 6/10
- Simplify: GCD of 6 and 10 is 2
- Divide: 6÷2 = 3, 10÷2 = 5
- Result: 3/5
Example 3: Convert 0.125 to Fraction
- Write decimal as fraction: 0.125 = 125/1000
- Simplify: GCD of 125 and 1000 is 125
- Divide: 125÷125 = 1, 1000÷125 = 8
- Result: 1/8
Common Decimal-Fraction Equivalents
| Decimal | Fraction | Simplified | Percentage |
|---|---|---|---|
| 0.1 | 1/10 | 1/10 | 10% |
| 0.2 | 2/10 | 1/5 | 20% |
| 0.25 | 25/100 | 1/4 | 25% |
| 0.5 | 5/10 | 1/2 | 50% |
| 0.75 | 75/100 | 3/4 | 75% |
| 0.333... | 1/3 | 1/3 | 33.33% |
| 0.666... | 2/3 | 2/3 | 66.67% |
Handling Different Decimal Types
Terminating Decimals
Decimals that end can be directly converted using place value.
- 0.25 → 25/100 → 1/4
- 0.8 → 8/10 → 4/5
- 0.375 → 375/1000 → 3/8
Repeating Decimals
Decimals with repeating patterns require algebraic methods.
- 0.333... → 1/3
- 0.666... → 2/3
- 0.142857142857... → 1/7
Applications in Real Life
Education & Academics
- Math problem solving
- Algebraic manipulations
- Geometry calculations
Daily Life & Practical Use
- Recipe measurements
- Construction and woodworking
- Financial calculations
- Measurement conversions
Frequently Asked Questions (FAQs)
Q: How do I convert repeating decimals to fractions?
A: Use algebraic equations. For example, for 0.333..., let x = 0.333..., then 10x = 3.333..., subtract to get 9x = 3, so x = 3/9 = 1/3.
Q: What if the decimal is greater than 1?
A: Convert to a mixed number. For example, 1.75 = 1 + 0.75 = 1 + 3/4 = 1¾.
Q: How accurate is the conversion?
A: For terminating decimals, it's exact. For repeating decimals, we provide the exact fraction.
Q: Can all decimals be converted to fractions?
A: Yes, all terminating and repeating decimals can be converted to exact fractions. Irrational numbers like π cannot be exactly represented as fractions.
Master decimal conversions with Toolivaa's free Decimal to Fraction Calculator, and explore more mathematical tools in our Math Calculators collection.