Decimal to Fraction Calculator
Convert any decimal to a simplified fraction
Calculator
Enter a decimal and get the simplified fraction instantly.
About the Decimal to Fraction Calculator
The Decimal to Fraction Calculator converts any decimal number into an equivalent simplified fraction. It works for both terminating and repeating decimals, helping students, engineers, teachers, and anyone working with numerical precision quickly obtain exact fractional values without manual calculation.
What You Can Calculate
- Simplified Fraction: Converts any decimal into the lowest-term fraction.
- Mixed Number Form: Shows the result as a whole number plus a fraction when applicable.
- Decimal Precision Handling: Supports long, repeating, or rounded decimal inputs.
- Step-by-Step Breakdown: Shows how the decimal is transformed into a fraction.
Formulas Used in the Calculator
The calculator applies standard mathematical procedures for decimal-to-fraction conversion:
- Terminating Decimals: Convert the decimal to an integer ratio and simplify: fraction = (decimal × 10ⁿ) / 10ⁿ
- Simplification: Both numerator and denominator are divided by the greatest common divisor (GCD).
- Mixed Numbers: When the numerator is greater than the denominator: whole = ⌊numerator / denominator⌋, remainder = numerator mod denominator.
How to Use the Calculator
- Enter any decimal value (e.g., 0.75, 3.125, 0.333...).
- The calculator immediately converts it to a simplified fraction.
- Review the mixed-number form and step-by-step details if displayed.
Applications of Decimal-to-Fraction Conversion
Converting decimals to fractions is essential in mathematics, engineering, construction, science, and education. Fractions often provide more accurate representations for measurements, ratios, and symbolic calculations. This tool helps ensure precision in technical drawings, formulas, manufacturing, and academic work.