How Many Sig Figs Calculator

Significant Figures Calculator

The number 12.00 has 4 significant figure(s).

Understanding Significant Figures

Significant figures (often abbreviated as 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 of measurements and calculations. When you perform calculations, the result should not imply greater precision than the least precise measurement used in the calculation.

Rules for Determining Significant Figures:

  1. Non-zero digits are always significant.
    Example: 123.45 has 5 significant figures.
  2. Zeros between non-zero digits are significant (sandwich zeros).
    Example: 1002.3 has 5 significant figures.
  3. Leading zeros (zeros before non-zero digits) are NOT significant. They only indicate the position of the decimal point.
    Example: 0.00123 has 3 significant figures (the 1, 2, and 3).
  4. Trailing zeros (zeros at the end of the number) are significant ONLY if the number contains a decimal point.
    Example: 12.00 has 4 significant figures. 120. has 3 significant figures.
  5. Trailing zeros in a number without a decimal point are generally considered NOT significant. This is because they are ambiguous; they might be placeholders.
    Example: 1200 has 2 significant figures (the 1 and 2). If you meant 4 sig figs, you would write 1200. or use scientific notation.
  6. Exact numbers have an infinite number of significant figures. These are numbers obtained by counting (e.g., 12 eggs) or by definition (e.g., 1 inch = 2.54 cm). This calculator focuses on measured or calculated values.
  7. Scientific Notation: All digits in the mantissa (the part before 'x 10^') are significant.
    Example: 1.23 x 10^4 has 3 significant figures. This calculator will process the mantissa (e.g., "1.23").

How to Use This Calculator:

Simply enter any number into the "Enter a Number" field. This can be an integer, a decimal, or a number with leading or trailing zeros. Click the "Calculate Significant Figures" button, and the calculator will instantly display the number of significant figures based on the rules outlined above.

Note on Ambiguity: For numbers like 1200 (without a decimal point), this calculator follows the common convention that trailing zeros are not significant. If you intend for them to be significant, you must include a decimal point (e.g., 1200.).

function calculateSigFigs() { var numberString = document.getElementById("numberInput").value; var originalNumberString = numberString; // 1. Handle empty input if (numberString.trim() === "") { document.getElementById("sigFigResult").innerHTML = "Please enter a number."; return; } // 2. Remove any leading/trailing whitespace numberString = numberString.trim(); // 3. Handle scientific notation (e.g., 1.23e-4) – only mantissa counts var eIndex = numberString.toLowerCase().indexOf('e'); if (eIndex !== -1) { numberString = numberString.substring(0, eIndex); } // 4. Remove any sign (+/-) if (numberString.startsWith('+') || numberString.startsWith('-')) { numberString = numberString.substring(1); } // 5. Check if it's a valid number after initial cleaning // This catches non-numeric inputs like "abc" or "1.2.3" if (isNaN(parseFloat(numberString)) || numberString === ".") { // parseFloat("." ) is NaN document.getElementById("sigFigResult").innerHTML = "Invalid number format. Please enter a valid number."; return; } // 6. Handle "0" or "0.0" cases if (parseFloat(numberString) === 0) { document.getElementById("sigFigResult").innerHTML = "The number " + originalNumberString + " has 1 significant figure (representing an exact zero)."; return; } var sigFigs = 0; var hasDecimal = numberString.includes('.'); var startedCounting = false; for (var i = 0; i `sigFigs` would be 4. Needs to be 2. if (!hasDecimal && startedCounting) { var tempNum = numberString; // Find the first non-zero digit var firstNonZeroIdx = -1; for (var k = 0; k = 0; k–) { if (tempNum[k] !== '0') { lastNonZeroIdx = k; break; } } if (firstNonZeroIdx !== -1) { sigFigs = lastNonZeroIdx – firstNonZeroIdx + 1; } else { // This case should be handled by parseFloat(numberString) === 0 earlier sigFigs = 0; // Should not happen for valid non-zero numbers } } document.getElementById("sigFigResult").innerHTML = "The number " + originalNumberString + " has " + sigFigs + " significant figure(s)."; } // Initialize the calculator with a default value on page load window.onload = function() { calculateSigFigs(); };

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