Decimals Into Fractions Calculator

Decimal to Fraction Converter

// GCD function (Euclidean algorithm) 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 convertDecimalToFraction() { var decimalStr = document.getElementById("decimalInput").value; var resultDiv = document.getElementById("result"); if (decimalStr.trim() === "") { resultDiv.innerHTML = "Please enter a decimal number."; resultDiv.style.backgroundColor = "#fff3cd"; // Warning color resultDiv.style.color = "#856404"; return; } var decimal = parseFloat(decimalStr); if (isNaN(decimal)) { resultDiv.innerHTML = "Invalid input. Please enter a valid number."; resultDiv.style.backgroundColor = "#f8d7da"; // Error color resultDiv.style.color = "#721c24"; return; } var isNegative = decimal < 0; decimal = Math.abs(decimal); // Handle integers (e.g., 5, 5.0, 5.) if (decimal % 1 === 0) { resultDiv.innerHTML = "The fraction is: " + (isNegative ? "-" : "") + decimal + "/1"; resultDiv.style.backgroundColor = "#e9f7ef"; // Success color resultDiv.style.color = "#28a745"; return; } // Determine the number of decimal places from the string representation var parts = decimalStr.split('.'); var fractionalPart = parts.length > 1 ? parts[1] : ""; var decimalPlaces = fractionalPart.length; // If the input was like "5." or "5.0", fractionalPart would be "" or "0" // The integer check above handles "5." and "5.0" correctly. // This part of the code is for actual fractional parts like "0.75" or "1.25". var numerator = parseInt(fractionalPart, 10); var denominator = Math.pow(10, decimalPlaces); // If there's an integer part, add it to the numerator to form an improper fraction var integerPart = Math.floor(decimal); if (integerPart > 0) { numerator = numerator + (integerPart * denominator); } // Find GCD to simplify the fraction var commonDivisor = gcd(numerator, denominator); var simplifiedNumerator = numerator / commonDivisor; var simplifiedDenominator = denominator / commonDivisor; var finalFraction = (isNegative ? "-" : "") + simplifiedNumerator + "/" + simplifiedDenominator; resultDiv.innerHTML = "The fraction is: " + finalFraction + ""; resultDiv.style.backgroundColor = "#e9f7ef"; // Success color resultDiv.style.color = "#28a745"; }

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. Each digit to the right of the decimal point represents a power of ten in the denominator. For example, 0.5 means five-tenths (5/10), 0.25 means twenty-five hundredths (25/100), and 0.125 means one hundred twenty-five thousandths (125/1000).

What is a Fraction?

A fraction represents a part of a whole or a collection of things. It consists of two numbers separated by a horizontal line: 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 instance, 1/2 means one out of two equal parts, and 3/4 means three out of four equal parts.

Why Convert Decimals to Fractions?

Converting decimals to fractions is a useful skill in various mathematical contexts and real-world applications:

• Precision: Fractions can represent exact values, especially for repeating decimals (though this calculator focuses on terminating decimals). For example, 1/3 is exact, while 0.333… is an approximation.
• Simplification: Fractions often simplify complex numbers into more manageable and understandable ratios.
• Algebra and Calculus: Many advanced mathematical operations are easier to perform with fractions than with decimals.
• Measurement: In fields like carpentry or cooking, fractions are often preferred for precise measurements (e.g., 1/4 inch, 1/2 cup).

How to Convert a Terminating Decimal to a Fraction (Manual Steps)

Here's the step-by-step process for converting a terminating decimal to a fraction:

1. Write down the decimal: For example, let's convert 0.75.
2. Determine the place value of the last digit: In 0.75, the last digit (5) is in the hundredths place.
3. Write the decimal as a fraction with a denominator of 10, 100, 1000, etc.: The denominator will be 1 followed by as many zeros as there are decimal places. For 0.75, there are two decimal places, so the denominator is 100. The numerator is the decimal number without the decimal point. So, 0.75 becomes 75/100.
4. Simplify the fraction: Find the greatest common divisor (GCD) of the numerator and the denominator, then divide both by the GCD.
   • For 75/100, the GCD of 75 and 100 is 25.
   • Divide the numerator: 75 ÷ 25 = 3.
   • Divide the denominator: 100 ÷ 25 = 4.
   • The simplified fraction is 3/4.
5. Handle whole numbers: If your decimal has a whole number part (e.g., 1.25), you can convert the fractional part first (0.25 = 1/4) and then combine it with the whole number to form a mixed number (1 1/4) or an improper fraction (5/4). Our calculator directly provides the improper fraction.

Examples:

• 0.5: The 5 is in the tenths place. So, 5/10. Simplified: 1/2.
• 0.125: The 5 is in the thousandths place. So, 125/1000. Simplified: 1/8.
• 1.2: The 2 is in the tenths place. So, 1 and 2/10. Simplified: 1 and 1/5, or as an improper fraction: 6/5.
• 0.004: The 4 is in the thousandths place. So, 4/1000. Simplified: 1/250.

Use the calculator above to quickly convert your decimal numbers into their simplest fractional forms!