Long Division Calculator with Steps (Decimals)
Perform long division and see each step broken down, including handling decimal remainders.
Steps and Result
Enter the dividend and divisor to see the long division process and the final answer.
Understanding Long Division with Decimals
Long division is a fundamental arithmetic method used to divide large numbers. It breaks down the division process into a series of simpler steps, making it manageable. When dealing with numbers that have decimal points, the process extends to find a more precise quotient.
How Long Division Works:
The core principle of long division is repeated subtraction and multiplication. It involves comparing the divisor with parts of the dividend, determining how many times the divisor fits into that part, multiplying, and then subtracting to find the remainder for the next step.
- Set up: Write the dividend inside the division bracket and the divisor outside to the left.
- Divide: Determine how many times the first digit (or group of digits) of the dividend can be divided by the divisor. Write this number above the dividend.
- Multiply: Multiply the digit you just wrote above by the divisor. Write the result below the part of the dividend you used.
- Subtract: Subtract the result from the corresponding part of the dividend.
- Bring Down: Bring down the next digit from the dividend and write it next to the remainder.
- Repeat: Repeat steps 2-5 with the new number until all digits of the dividend have been used.
Handling Decimals:
When the dividend has a decimal point or when you need a more precise answer, you can extend the long division process:
- Add a Decimal Point: Place a decimal point in the quotient directly above the decimal point in the dividend.
- Append Zeros: If you run out of digits in the dividend and still have a remainder, add a decimal point to the dividend and append zeros (e.g., 123 becomes 123.000). Then, continue bringing down these zeros to continue the division process.
- Repeating or Terminating Decimals: The division may result in a terminating decimal (it ends) or a repeating decimal (a pattern of digits repeats infinitely). You might need to round the answer to a certain number of decimal places for practical use.
When is Long Division Useful?
- Education: It's a core mathematical skill taught in schools to build number sense and algorithmic thinking.
- Manual Calculations: Useful when a calculator is unavailable or for understanding the underlying mechanics of division.
- Complex Fractions: Converting fractions to decimals often relies on long division.
- Problem Solving: Many word problems require division to find quantities, averages, or ratios.
This calculator provides a clear, step-by-step breakdown, making the process of long division with decimals easier to understand and verify.
Steps and Result
"; // Input Validation if (dividendInput === "" || divisorInput === "") { stepsHtml += "Please enter both the dividend and the divisor."; resultDiv.innerHTML = stepsHtml; return; } var dividend = parseFloat(dividendInput); var divisor = parseFloat(divisorInput); if (isNaN(dividend) || isNaN(divisor)) { stepsHtml += "Invalid number format. Please enter valid numbers."; resultDiv.innerHTML = stepsHtml; return; } if (divisor === 0) { stepsHtml += "Error: Division by zero is not allowed."; resultDiv.innerHTML = stepsHtml; return; } // Handle signs – we'll perform division on positive numbers and apply sign at the end var dividendSign = dividend < 0 ? -1 : 1; var divisorSign = divisor < 0 ? -1 : 1; var finalSign = dividendSign * divisorSign; dividend = Math.abs(dividend); divisor = Math.abs(divisor); var quotient = 0; var remainder = dividend; var currentStep = 0; var decimalPlaces = 0; // Track decimal places for precision var maxDecimalPlaces = 10; // Limit decimal places to avoid infinite loops for repeating decimals // For displaying the division setup visually var divisionSetup = "1. Setup:";
divisionSetup += " " + divisor.toString().padStart(remainder.toString().length + 2) + ") " + dividend.toString() + "";
divisionSetup += " " + "-".repeat(Math.max(dividend.toString().length, divisor.toString().length) + 2) + "";
divisionSetup += "
";
stepsHtml += divisionSetup;
// Integer part of the division
var dividendStr = dividend.toString();
var divisorStr = divisor.toString();
var wholePartDividend = dividendStr.includes('.') ? dividendStr.split('.')[0] : dividendStr;
var fractionalPartDividend = dividendStr.includes('.') ? dividendStr.split('.')[1] : ";
var currentDividendPart = "";
var quotientPart = "";
for (var i = 0; i = divisor) {
var factor = Math.floor(currentDividendNum / divisor);
quotientPart += factor.toString();
var product = factor * divisor;
var remainderStep = currentDividendNum – product;
var stepDesc = "Step " + (currentStep + 1) + ":";
stepDesc += " Take '" + currentDividendPart + "' from dividend.";
stepDesc += " " + divisor + " goes into " + currentDividendPart + " " + factor + " times.";
stepDesc += " " + factor + " * " + divisor + " = " + product + "";
stepDesc += " " + currentDividendPart + "";
stepDesc += " – " + product.toString().padStart(currentDividendPart.length) + "";
stepDesc += " " + "-".repeat(Math.max(currentDividendPart.length, product.toString().length)) + "";
stepDesc += " Remainder: " + remainderStep + "";
stepDesc += "
";
stepsHtml += stepDesc;
remainder = remainderStep;
currentDividendPart = remainderStep.toString(); // Start next part with the remainder
currentStep++;
} else {
if (i < wholePartDividend.length) { // Only add quotient digit if we are past initial insufficient digits
quotientPart += "0";
}
var stepDesc = "Step " + (currentStep + 1) + ":";
stepDesc += " '" + currentDividendPart + "' is less than " + divisor + ". Take next digit.";
stepDesc += "
";
// Only add if it's not just an initial zero before the first digit
if (currentDividendPart.length > 1 || quotientPart.length > 0) {
stepsHtml += stepDesc;
}
}
}
// If the whole part resulted in zero quotient (e.g. 0.5 / 2)
if (quotientPart === "" && dividend < divisor) {
quotientPart = "0";
stepsHtml += "Step " + (currentStep + 1) + ":";
stepsHtml += " Dividend is smaller than divisor. Quotient starts with 0.";
stepsHtml += "
";
currentStep++;
}
quotient = parseFloat(quotientPart);
// Handling the decimal part
var currentDividendForDecimal = currentDividendPart === "" ? "0" : currentDividendPart; // Start with previous remainder or 0
var fractionalIndex = 0;
// Add the decimal point to quotient if there's a remainder and we are going into decimals
if (remainder > 0 || fractionalPartDividend.length > 0) {
if (quotientPart.length > 0 && quotientPart !== "0") { // Only add decimal if there's a whole part quotient
stepsHtml += "Step " + (currentStep + 1) + ":";
stepsHtml += " Add decimal point to quotient. Bring down next digit (or zero).";
stepsHtml += "
";
currentStep++;
}
if (quotientPart === "0") { // Special case: if whole part is 0
stepsHtml += "Step " + (currentStep + 1) + ":";
stepsHtml += " Add decimal point to quotient (0.). Bring down next digit (or zero).";
stepsHtml += "
";
currentStep++;
}
// Ensure quotient starts with 0. if it's just .something
if(quotientPart === "" || quotientPart === "0") quotient = 0; // Ensure quotient is 0 if no whole part was found yet
}
while ((remainder > 0 || fractionalIndex < fractionalPartDividend.length) && decimalPlaces < maxDecimalPlaces) {
var nextDigit = "";
if (fractionalIndex < fractionalPartDividend.length) {
nextDigit = fractionalPartDividend[fractionalIndex];
fractionalIndex++;
} else {
// If we've exhausted original fractional digits, append zeros
nextDigit = "0";
}
currentDividendForDecimal += nextDigit;
var currentDividendNum = parseFloat(currentDividendForDecimal);
var stepDesc = "Step " + (currentStep + 1) + ":";
if (currentDividendNum >= divisor) {
var factor = Math.floor(currentDividendNum / divisor);
quotientPart += factor.toString();
var product = factor * divisor;
remainder = currentDividendNum – product;
stepDesc += " Bring down '" + nextDigit + "'. New number is '" + currentDividendForDecimal + "'.";
stepDesc += " " + divisor + " goes into " + currentDividendForDecimal + " " + factor + " times.";
stepDesc += " " + factor + " * " + divisor + " = " + product + "";
stepDesc += " " + currentDividendNum.toString().padStart(currentDividendForDecimal.length) + "";
stepDesc += " – " + product.toString().padStart(currentDividendForDecimal.length) + "";
stepDesc += " " + "-".repeat(Math.max(currentDividendForDecimal.length, product.toString().length)) + "";
stepDesc += " Remainder: " + remainder + "";
currentDividendForDecimal = remainder.toString(); // Start next part with the remainder
decimalPlaces++;
} else {
quotientPart += "0";
stepDesc += " Bring down '" + nextDigit + "'. New number is '" + currentDividendForDecimal + "'.";
stepDesc += " " + currentDividendForDecimal + " is less than " + divisor + ". Write 0 in quotient.";
remainder = currentDividendNum; // Remainder is the number itself if smaller than divisor
}
stepsHtml += stepDesc + "
";
currentStep++;
// If remainder is 0 and we've used all original fractional digits, we can stop unless we want more precision
if (remainder === 0 && fractionalIndex >= fractionalPartDividend.length && fractionalPartDividend.length > 0) {
// Optionally continue by adding zeros if more decimal places are desired
// For now, we stop if remainder is 0 and all digits are used
}
}
// Format the final quotient
var finalQuotient = parseFloat(quotientPart.split(").join(")); // Ensure it's a number
if (decimalPlaces > 0) {
var decimalPart = quotientPart.substring(quotientPart.length – decimalPlaces);
finalQuotient = parseFloat(quotientPart.substring(0, quotientPart.length – decimalPlaces) + "." + decimalPart);
} else if (quotientPart.includes('.')) {
finalQuotient = parseFloat(quotientPart);
} else {
// If no decimal calculation occurred, ensure quotient is integer
finalQuotient = parseInt(quotientPart, 10);
}
// Re-apply the sign
finalQuotient = finalQuotient * finalSign;
// Display remainder if any and if it's not zero after max decimal places
var finalRemainder = "";
if (remainder > 0 && decimalPlaces >= maxDecimalPlaces) {
finalRemainder = " (with a remainder of " + remainder.toFixed(maxDecimalPlaces) + ")";
} else if (remainder > 0 && decimalPlaces = fractionalPartDividend.length && fractionalPartDividend.length > 0) {
// Exact division, no remainder after original digits
}
// Construct the final output string
var displayQuotient = isNaN(finalQuotient) ? "N/A" : finalQuotient.toString();
// Append final result summary
stepsHtml += "Result: " + displayQuotient + finalRemainder + "";
stepsHtml += "Note: Calculations may be rounded or truncated after " + maxDecimalPlaces + " decimal places for repeating decimals.";
resultDiv.innerHTML = stepsHtml;
}