Decimal to Fraction Calculator
Convert decimal numbers to simplified fractions with step-by-step solutions
Examples: 0.5, 0.75, 2.5, 0.333, 0.125
How to Use This Calculator
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What This Calculator Does
This calculator converts decimal numbers to their simplified fraction equivalents. It handles terminating decimals (like 0.75), repeating decimals (like 0.333...), and mixed numbers (like 2.5). The calculator shows you the exact steps to perform the conversion, making it perfect for learning and homework help.
Example Problems
Common Decimal Conversions:
- 0.5 = 1/2 (one half - common in cooking measurements)
- 0.25 = 1/4 (one quarter - quarters and coins)
- 0.75 = 3/4 (three quarters - recipe adjustments)
- 0.125 = 1/8 (one eighth - woodworking measurements)
- 0.333 ≈ 1/3 (one third - dividing into three parts)
Mixed Number Conversions:
- 2.5 = 5/2 or 2 1/2 (two and a half hours)
- 3.75 = 15/4 or 3 3/4 (measurement conversions)
- 1.25 = 5/4 or 1 1/4 (recipe scaling)
How Decimal to Fraction Conversion Works
Converting a decimal to a fraction involves these steps:
- Count the number of decimal places in your decimal
- Write the decimal as a fraction with a denominator of 10, 100, 1000, etc. (based on decimal places)
- Find the Greatest Common Divisor (GCD) of the numerator and denominator
- Divide both the numerator and denominator by the GCD to simplify
- If the result has a whole number part, optionally express it as a mixed number
Frequently Asked Questions
How do I convert decimals to fractions?
To convert a decimal to a fraction: (1) Count decimal places, (2) Write as fraction over 10, 100, etc., (3) Simplify by dividing numerator and denominator by their GCD. For example, 0.75 has 2 decimal places, so it's 75/100. The GCD of 75 and 100 is 25, so dividing both by 25 gives 3/4.
What is a terminating decimal?
A terminating decimal is a decimal that has a finite number of digits after the decimal point. Examples include 0.5, 0.75, and 0.125. These decimals can always be converted to exact fractions. Non-terminating decimals (like 0.333...) repeat forever and can only be approximated as fractions.
What is a repeating decimal?
A repeating decimal has one or more digits that repeat infinitely. For example, 0.333... (where 3 repeats) equals 1/3, and 0.666... equals 2/3. Our calculator handles common repeating decimals by recognizing patterns and converting them to their exact fraction equivalents.
How do I simplify fractions?
To simplify a fraction, find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by the GCD. For example, to simplify 75/100: the GCD is 25, so 75÷25 = 3 and 100÷25 = 4, giving you 3/4. Our calculator automatically simplifies all fractions for you.
What's the difference between improper fractions and mixed numbers?
An improper fraction has a numerator larger than or equal to its denominator (like 5/2). A mixed number combines a whole number with a fraction (like 2 1/2). They represent the same value, just in different forms. For example, 5/2 = 2 1/2. Our calculator shows both forms when applicable.
Why use a decimal to fraction converter?
A decimal to fraction converter is essential for cooking (converting 0.5 cups to 1/2 cup), construction and woodworking (converting measurements), homework help (showing your work), and any situation where fractions are more practical than decimals. It saves time and ensures accuracy.
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Educational Disclaimer
This calculator is provided for educational purposes and homework assistance. While we strive for accuracy, please verify critical calculations independently. Results should not be used as the sole basis for important financial, academic, or professional decisions. Always check your work and consult with appropriate professionals when needed.