Decimal Into Fraction Calculator

Decimal to Fraction Converter

function gcd(a, b) { if (b === 0) { return a; } return gcd(b, a % b); } function calculateFraction() { var decimalString = document.getElementById("decimalInput").value; var decimalNum = parseFloat(decimalString); var resultDiv = document.getElementById("result"); if (isNaN(decimalNum)) { resultDiv.innerHTML = "Please enter a valid number."; return; } if (decimalNum === 0) { resultDiv.innerHTML = "0/1"; return; } var isNegative = decimalNum 1 ? parts[1] : ""; var decimalPlaces = fractionalPartString.length; // Handle cases like "1." or ".5" if (parts.length === 1 && decimalString.indexOf('.') !== -1) { // e.g., "5." decimalPlaces = 0; // Treat as integer } else if (parts.length > 1 && fractionalPartString === "") { // e.g., "5." decimalPlaces = 0; } else if (parts.length === 1 && decimalString.indexOf('.') === -1) { // e.g., "5" decimalPlaces = 0; } var numerator; var denominator; if (decimalPlaces === 0) { numerator = integerPart; denominator = 1; } else { // Construct the full number as an integer by removing the decimal point // and then determine the denominator based on decimal places. var fullNumberString = (integerPart === 0 && decimalString.startsWith("0.")) ? fractionalPartString : (integerPart + fractionalPartString); numerator = parseInt(fullNumberString); denominator = Math.pow(10, decimalPlaces); } // Simplify the fraction 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 fundamental ways to represent numbers that are not whole. While decimals use a base-10 system with a decimal point to denote fractional parts, fractions express a part of a whole as a ratio of two integers: a numerator and a denominator.

What is a Decimal?

A decimal number is a number that includes a decimal point, separating the whole number part from the fractional part. For example, in 0.75, '0' is the whole number part, and '75' is the fractional part. Each digit after the decimal point represents a power of ten: the first digit is tenths (1/10), the second is hundredths (1/100), the third is thousandths (1/1000), and so on.

What is a Fraction?

A fraction represents a part of a whole or a collection. It consists of two numbers separated by a horizontal line or a slash: the numerator (the top number) and the denominator (the bottom number). The numerator tells you how many parts you have, and the denominator tells you how many equal parts make up the whole. For example, 3/4 means three out of four equal parts.

Why Convert Decimals to Fractions?

Converting decimals to fractions is useful for several reasons:

• Precision: Fractions can represent exact values, especially for repeating decimals (e.g., 0.333… is exactly 1/3), whereas decimals often require rounding.
• Mathematical Operations: Sometimes, performing calculations with fractions can be simpler or more accurate than with decimals, particularly in algebra or when dealing with exact ratios.
• Understanding Ratios: Fractions inherently express ratios, which can be more intuitive in certain contexts, like recipes or proportions.

How the Calculator Works (Step-by-Step Conversion)

Our Decimal to Fraction Converter uses a straightforward method to transform a decimal into its simplest fractional form:

1. Identify the Decimal Places: The calculator first determines how many digits are after the decimal point. This number dictates the initial denominator. For example, 0.75 has two decimal places, so the initial denominator will be 100. 1.25 also has two decimal places, so its initial denominator is 100.
2. Form the Initial Fraction:
   • If the decimal is 0.75, the numerator becomes 75 and the denominator becomes 100, forming 75/100.
   • If the decimal is 1.25, the whole number part (1) is combined with the fractional part (25). This is equivalent to (1 * 100 + 25) / 100, resulting in 125/100.
3. Simplify the Fraction: The final step is to simplify the fraction to its lowest terms. This is done by finding the Greatest Common Divisor (GCD) of the numerator and the denominator and then dividing both by the GCD.
   • For 75/100, the GCD of 75 and 100 is 25. Dividing both by 25 gives 3/4.
   • For 125/100, the GCD of 125 and 100 is 25. Dividing both by 25 gives 5/4.

Examples:

• Input: 0.5
  Decimal places: 1. Initial fraction: 5/10. GCD(5, 10) = 5. Simplified fraction: 1/2.
• Input: 0.25
  Decimal places: 2. Initial fraction: 25/100. GCD(25, 100) = 25. Simplified fraction: 1/4.
• Input: 1.75
  Decimal places: 2. Initial fraction: 175/100. GCD(175, 100) = 25. Simplified fraction: 7/4.
• Input: 0.125
  Decimal places: 3. Initial fraction: 125/1000. GCD(125, 1000) = 125. Simplified fraction: 1/8.
• Input: 0.333 (approximation of 1/3)
  Decimal places: 3. Initial fraction: 333/1000. GCD(333, 1000) = 1. Simplified fraction: 333/1000. (Note: For true repeating decimals like 0.333…, this calculator provides an approximation based on the input's precision.)

Use the calculator above to quickly convert any terminating decimal into its simplest fractional form!