Expanded Form Calculator

Expanded Form Calculator

Result:

function calculateExpandedForm() { var input = document.getElementById("numInput").value.trim(); var resultBox = document.getElementById("resultBox"); var expandedText = document.getElementById("expandedText"); var detailedBreakdown = document.getElementById("detailedBreakdown"); if (input === "" || isNaN(input)) { alert("Please enter a valid numeric value."); return; } var parts = input.split("."); var integerPart = parts[0].replace(/^0+/, ""); if (integerPart === "") integerPart = "0"; var decimalPart = parts.length > 1 ? parts[1] : ""; var expandedArray = []; var breakdownArray = []; // Process Integer Part for (var i = 0; i < integerPart.length; i++) { var digit = integerPart[i]; if (digit !== "0") { var power = integerPart.length – 1 – i; var value = digit * Math.pow(10, power); expandedArray.push(value.toString()); breakdownArray.push("(" + digit + " × " + Math.pow(10, power).toLocaleString() + ")"); } } // Process Decimal Part for (var j = 0; j < decimalPart.length; j++) { var digitD = decimalPart[j]; if (digitD !== "0") { var denominator = Math.pow(10, j + 1); expandedArray.push((digitD / denominator).toString()); breakdownArray.push("(" + digitD + " × 1/" + denominator.toLocaleString() + ")"); } } if (expandedArray.length === 0) { expandedText.innerText = "0"; detailedBreakdown.innerHTML = "0"; } else { expandedText.innerText = expandedArray.join(" + "); detailedBreakdown.innerHTML = "Multiplication Form:" + breakdownArray.join(" + "); } resultBox.style.display = "block"; }

What is Expanded Form?

In mathematics, expanded form is a way of writing a number to show the value of each digit. It is expressed as a sum of each digit multiplied by its matching place value (units, tens, hundreds, thousands, tenths, hundredths, etc.).

How to Write Numbers in Expanded Form

To convert a standard number into its expanded version, you must identify the position of every digit. For example, in the number 5,284:

  • The 5 is in the thousands place (5,000)
  • The 2 is in the hundreds place (200)
  • The 8 is in the tens place (80)
  • The 4 is in the ones place (4)

The expanded form is: 5,000 + 200 + 80 + 4.

Expanded Form with Decimals

Decimals follow the same logic but move into fractions of ten. For the number 12.34:

  • 10 + 2 (Integer part)
  • 0.3 (3/10 or three-tenths)
  • 0.04 (4/100 or four-hundredths)

Result: 10 + 2 + 0.3 + 0.04.

Why Use the Expanded Form Calculator?

This tool is essential for students learning place value and scientific notation. It helps visualize how large numbers are constructed and simplifies the process of understanding decimals. It supports both whole numbers and complex decimals, providing both the additive result and the multiplicative breakdown.

Standard Form Expanded Form
158 100 + 50 + 8
4,025 4,000 + 20 + 5
0.729 0.7 + 0.02 + 0.009
61.04 60 + 1 + 0.04

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