Decimal to Fraction Calculator
Convert any decimal number into a simplified proper fraction, improper fraction, or mixed number.
Decimal to Fraction — interactive calculator, computed instantly in your browser.
How to Convert Decimals to Simplified Fractions & Mixed Numbers
Place-Value Reduction Workflow
Simplification Process: Express decimal over $10^n$ (where $n$ is decimal places), then divide both numerator and denominator by their Greatest Common Divisor (GCD).
Converting decimals into simplified fractions is essential in carpentry, machining, mechanical engineering, and exact mathematical analysis where fractional measurements (such as $5/8"$ or $7/16"$) are standard.
1. Step-by-Step Conversion Algorithm
- Count Decimal Digits ($d$): Identify number of digits following decimal point (e.g. $0.375$ has $d=3$).
- Form Base Fraction: Set numerator as integer digits and denominator as $10^d$ (e.g. $\frac{375}{10^3} = \frac{375}{1000}$).
- Compute Greatest Common Divisor (GCD): Calculate $\text{GCD}(375, 1000) = 125$.
- Divide by GCD: $\frac{375 \div 125}{1000 \div 125} = \mathbf{\frac{3}{8}}$.
2. Repeating Decimal Algebraic Formula
To convert a repeating decimal like $x = 0.\overline{63}$:
🔗 Rational Decimal Conversions
Decimal-to-fraction conversions identify exact rational quotients from floating-point measurements. Visit our ➗ Math Hub for algebra tools.
Calculate fraction operations or solve proportions using the cross-references below.
Frequently Asked Questions (Decimal to Fraction)
Fractions represent exact rational numbers without rounding error. $1/3$ is exact, whereas $0.3333$ introduces compounding errors when multiplied over hundreds of tolerances.
Carry the negative sign to the final numerator. For instance, $-2.75 = -2 \frac{75}{100} = -2 \frac{3}{4} = -\frac{11}{4}$.