Decimal to Fraction Calculator

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Decimal to Fraction Calculator

Result:

function calculateFraction() { var input = document.getElementById('decimalInput').value.trim(); var resultDiv = document.getElementById('calc-result'); var fractionOutput = document.getElementById('fractionOutput'); var mixedOutput = document.getElementById('mixedNumberOutput'); var stepsOutput = document.getElementById('simplifiedSteps'); if (input === "" || isNaN(input)) { alert("Please enter a valid decimal number."); return; } var val = parseFloat(input); var isNegative = val simpleDenominator && simpleDenominator !== 1) { var whole = Math.floor(simpleNumerator / simpleDenominator); var rem = simpleNumerator % simpleDenominator; var sign = isNegative ? "-" : ""; mixedOutput.innerHTML = "Mixed Number: " + sign + whole + " " + rem + "/" + simpleDenominator; } else if (simpleDenominator === 1) { mixedOutput.innerHTML = "Integer: " + finalNumerator; } else { mixedOutput.innerHTML = ""; } stepsOutput.innerHTML = "Simplified by dividing both numerator (" + numerator + ") and denominator (" + denominator + ") by their greatest common divisor: " + commonDivisor; }

How to Convert a Decimal to a Fraction

Converting a decimal to a fraction is a fundamental mathematical process that helps in visualizing ratios and performing precise calculations. Whether you are dealing with recipes, construction measurements, or financial modeling, understanding how decimals relate to fractions is essential.

Step-by-Step Conversion Process

  1. Identify the Place Value: Determine the place value of the last digit in the decimal. For example, in 0.85, the 5 is in the hundredths place.
  2. Create the Initial Fraction: Write the decimal as a numerator and its place value as the denominator. For 0.85, this becomes 85/100.
  3. Find the Greatest Common Divisor (GCD): Identify the largest number that divides both the numerator and the denominator evenly. For 85 and 100, the GCD is 5.
  4. Simplify: Divide both numbers by the GCD to get the simplest form. 85 ÷ 5 = 17, and 100 ÷ 5 = 20. The final fraction is 17/20.

Common Decimal to Fraction Examples

Decimal Fraction Simplified Fraction
0.5 5/10 1/2
0.25 25/100 1/4
0.125 125/1000 1/8
0.75 75/100 3/4

Why Use This Calculator?

While basic conversions can be done mentally, complex decimals like 0.3125 or large numbers like 4.5625 require more effort to simplify. This calculator handles the heavy lifting by finding the Greatest Common Divisor instantly, ensuring your fraction is always in its most reduced form. It also provides mixed numbers for decimals greater than 1, which is incredibly helpful for woodworking and standard measurement tasks.

Frequently Asked Questions

Q: Can this convert repeating decimals?
A: This specific tool is designed for terminating decimals (decimals that end). For repeating decimals like 0.333…, the math requires a different algebraic approach (e.g., 0.333… = 1/3).

Q: What is a simplified fraction?
A: A simplified fraction (or reduced fraction) is one where the numerator and denominator have no common factors other than 1.

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