Decimal to Fraction Calculator
Convert decimals to fractions instantly with automatic simplification and step-by-step explanations. Works with terminating and repeating decimals.
Decimal to Fraction Calculator
How to Use This Calculator
Enter any decimal number and the calculator will convert it to a fraction, automatically simplify it to lowest terms, and show it as a mixed number if applicable. Step-by-step conversion process is displayed for educational purposes.
Understanding Decimal to Fraction Conversion
To convert a decimal to a fraction, count the decimal places to determine the denominator (10, 100, 1000, etc.), use the decimal digits as the numerator, then simplify. For example, 0.75 has 2 decimal places, so it becomes 75/100, which simplifies to 3/4.
The Simplification Process
After creating the initial fraction, we find the Greatest Common Divisor (GCD) of the numerator and denominator. Dividing both by the GCD gives the simplified fraction. For example, 75/100 รท 25/25 = 3/4. This ensures the fraction is in its lowest terms.
Common Applications
Used in cooking and baking (converting recipe measurements), construction and carpentry (precise measurements), financial calculations, educational mathematics, data analysis, engineering calculations, and anywhere fractional representation is preferred over decimals.
Mixed Numbers vs Improper Fractions
If the decimal is greater than or equal to 1, the result can be shown as a mixed number (whole number plus fraction) or improper fraction (numerator larger than denominator). For example, 2.5 = 2 1/2 (mixed) or 5/2 (improper). Both forms are mathematically equivalent.
Frequently Asked Questions
Q: Can I convert repeating decimals? A: Yes, but calculator works best with terminating decimals. Q: What about negative decimals? A: Fully supported, result will be negative fraction. Q: Why simplify? A: Simplified fractions are easier to work with and understand. Q: Can I convert whole numbers? A: Yes, results in fraction with denominator 1.