Sig Figs Calculator

Significant Figures Calculator

function calculateSigFigs() { var inputNumberStr = document.getElementById("inputNumber").value; var desiredSigFigsStr = document.getElementById("desiredSigFigs").value; var resultDiv = document.getElementById("result"); // Input validation if (inputNumberStr.trim() === "" || desiredSigFigsStr.trim() === "") { resultDiv.innerHTML = "Please enter both a number and desired significant figures."; return; } var num = parseFloat(inputNumberStr); var n = parseInt(desiredSigFigsStr, 10); if (isNaN(num)) { resultDiv.innerHTML = "Invalid number entered. Please enter a numeric value."; return; } if (isNaN(n) || n <= 0 || !Number.isInteger(n)) { resultDiv.innerHTML = "Desired Significant Figures must be a positive integer."; return; } var roundedNumString; try { // The toPrecision() method formats a number to a specified length. // It rounds the number to n significant figures and returns a string. roundedNumString = num.toPrecision(n); } catch (e) { resultDiv.innerHTML = "Error during calculation: " + e.message + ""; return; } var output = "

Calculation Result:

"; output += "Original Number: " + inputNumberStr + ""; output += "Desired Significant Figures: " + n + ""; output += "Number Rounded to " + n + " Significant Figures: " + roundedNumString + ""; resultDiv.innerHTML = output; }

Understanding Significant Figures

Significant figures (often called "sig figs") are the digits in a number that carry meaning contributing to its precision. They are crucial in scientific and engineering fields to express the accuracy and precision of measurements and calculations. Using the correct number of significant figures ensures that results do not imply a greater precision than the original data.

Rules for Identifying Significant Figures:

1. Non-zero digits are always significant.
   Example: 458 cm has 3 significant figures.
2. Zeros between non-zero digits are significant.
   Example: 2005 kg has 4 significant figures.
3. Leading zeros (zeros before non-zero digits) are NOT significant. They only indicate the position of the decimal point.
   Example: 0.0025 g has 2 significant figures (2 and 5).
4. Trailing zeros (zeros at the end of the number) are significant ONLY if the number contains a decimal point.
   Example: 12.00 m has 4 significant figures.
   Example: 100.0 mL has 4 significant figures.
5. Trailing zeros in a number without a decimal point are generally NOT considered significant.
   Example: 1200 g has 2 significant figures (1 and 2). To make the zeros significant, you would write it in scientific notation (e.g., 1.20 x 10³ g for 3 sig figs, or 1.200 x 10³ g for 4 sig figs).

Rules for Rounding to Significant Figures:

When rounding a number to a specific number of significant figures, follow these steps:

1. Identify the significant figures: Determine which digits are significant based on the rules above.
2. Count from the first non-zero digit: Start counting significant figures from the first non-zero digit.
3. Look at the next digit:
   • If the digit immediately to the right of your desired last significant figure is 5 or greater, round up the last significant figure.
   • If it is less than 5, keep the last significant figure as it is.
4. Replace remaining digits:
   • For integers, replace any digits to the right of the rounded significant figure with zeros up to the decimal point.
   • For decimals, simply drop any digits to the right of the rounded significant figure.

Examples of Rounding:

• Round 123.45 to 3 significant figures:
  The first three significant figures are 1, 2, 3. The next digit is 4 (less than 5).
  Result: 123
• Round 0.001238 to 3 significant figures:
  The first non-zero digit is 1. The first three significant figures are 1, 2, 3. The next digit is 8 (5 or greater).
  Result: 0.00124
• Round 45678 to 2 significant figures:
  The first two significant figures are 4, 5. The next digit is 6 (5 or greater). Round up 5 to 6. Replace remaining digits with zeros.
  Result: 46000
• Round 1.20 to 2 significant figures:
  The first two significant figures are 1, 2. The next digit is 0 (less than 5).
  Result: 1.2
• Round 1.20 to 3 significant figures:
  The first three significant figures are 1, 2, 0.
  Result: 1.20 (The trailing zero is significant because of the decimal point).

Our Significant Figures Calculator helps you quickly round any number to your desired level of precision, making it an invaluable tool for students, scientists, and engineers.