Change to Fraction Calculator

Decimal to Fraction Converter

function gcd(a, b) { a = Math.abs(a); b = Math.abs(b); while (b) { var temp = b; b = a % b; a = temp; } return a; } function calculateFraction() { var decimalInput = document.getElementById("decimalNumber").value; var decimalNum = parseFloat(decimalInput); var resultDiv = document.getElementById("fractionResult"); if (isNaN(decimalNum)) { resultDiv.innerHTML = "Please enter a valid number."; return; } if (decimalNum === 0) { resultDiv.innerHTML = "0/1"; return; } var isNegative = decimalNum < 0; decimalNum = Math.abs(decimalNum); var decimalStr = decimalNum.toString(); var decimalPlaces = 0; if (decimalStr.includes('.')) { decimalPlaces = decimalStr.split('.')[1].length; } var numerator = decimalNum * Math.pow(10, decimalPlaces); var denominator = Math.pow(10, decimalPlaces); // Handle cases where floating point precision might cause issues // For example, 0.1 might become 0.10000000000000000555 // We need to ensure numerator is an integer numerator = Math.round(numerator); var commonDivisor = gcd(numerator, denominator); var simplifiedNumerator = numerator / commonDivisor; var simplifiedDenominator = denominator / commonDivisor; var sign = isNegative ? "-" : ""; resultDiv.innerHTML = sign + simplifiedNumerator + "/" + simplifiedDenominator; }

Understanding Decimals and Fractions

Decimals and fractions are two different ways to represent numbers that are not whole numbers. While decimals use a base-10 system with a decimal point to denote parts of a whole (e.g., 0.5, 0.75), fractions represent parts of a whole using a numerator (the top number) and a denominator (the bottom number), like 1/2 or 3/4.

Why Convert Decimals to Fractions?

Converting decimals to fractions can be incredibly useful in various situations:

• Precision: Fractions often provide an exact representation of a number, especially for repeating decimals (e.g., 1/3 is exact, while 0.333… is an approximation).
• Mathematical Operations: Sometimes, performing calculations with fractions (like adding or multiplying) can be simpler or more accurate than with decimals, particularly when dealing with common denominators.
• Understanding Relationships: Fractions can make it easier to visualize parts of a whole or compare quantities in a more intuitive way. For instance, knowing something is "one-quarter" (1/4) might be clearer than "zero point two five" (0.25) in certain contexts.
• Real-World Applications: Many recipes, measurements, and engineering specifications still use fractions, making conversion essential for practical tasks.

How the Conversion Works (Conceptually)

The process of converting a decimal to a fraction involves a few key steps:

1. Identify the Decimal Places: Count how many digits are after the decimal point. This number determines the initial denominator.
2. Form the Initial Fraction: Place the decimal number (without the decimal point) over a power of 10. For example, if there are two decimal places, the denominator will be 100 (10²); if three, it will be 1000 (10³), and so on. So, 0.75 becomes 75/100.
3. Simplify the Fraction: Find the Greatest Common Divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. Divide both numbers by their GCD to reduce the fraction to its simplest form. For 75/100, the GCD is 25, so 75 ÷ 25 = 3 and 100 ÷ 25 = 4, resulting in 3/4.

Examples:

• 0.5: One decimal place. Becomes 5/10. GCD(5, 10) = 5. Simplified: 1/2.
• 0.25: Two decimal places. Becomes 25/100. GCD(25, 100) = 25. Simplified: 1/4.
• 1.2: One decimal place. Becomes 12/10. GCD(12, 10) = 2. Simplified: 6/5.
• 0.375: Three decimal places. Becomes 375/1000. GCD(375, 1000) = 125. Simplified: 3/8.
• -0.75: Two decimal places. Becomes -75/100. GCD(75, 100) = 25. Simplified: -3/4.

This calculator automates these steps, providing you with the simplest fractional form of any decimal number you input.