Sigfig Calculator

Significant Figures Calculator

Results:

Number of Significant Figures: –

Rounded Number: –

Please enter a valid number.
function countSigFigs(numStr) { numStr = numStr.trim(); // Handle empty string or non-numeric input if (!numStr || isNaN(parseFloat(numStr))) { return 0; } // Special case for '0' or '0.0' etc. if (parseFloat(numStr) === 0) { return 1; // The number 0 has one significant figure by convention. } // Remove sign for processing var absNumStr = numStr.replace(/^[+-]/, "); var hasDecimal = absNumStr.includes('.'); // Remove decimal point for easier processing of digits var digitsOnly = absNumStr.replace('.', "); // Find first non-zero digit var firstNonZeroIndex = -1; for (var i = 0; i = 0; i–) { if (digitsOnly[i] !== '0') { lastNonZeroIndex = i; break; } } // Count digits from first non-zero to last non-zero (inclusive) return (lastNonZeroIndex – firstNonZeroIndex) + 1; } } function calculateSigFigs() { var inputNumberStr = document.getElementById('inputNumber').value; var roundToSigFigsStr = document.getElementById('roundToSigFigs').value; var sigFigCountElement = document.getElementById('sigFigCount'); var roundedNumberElement = document.getElementById('roundedNumber'); var errorMessageElement = document.getElementById('errorMessage'); sigFigCountElement.innerHTML = 'Number of Significant Figures: -'; roundedNumberElement.innerHTML = 'Rounded Number: -'; errorMessageElement.style.display = 'none'; var numVal = parseFloat(inputNumberStr); if (isNaN(numVal) || inputNumberStr.trim() === ") { errorMessageElement.style.display = 'block'; return; } var sigFigs = countSigFigs(inputNumberStr); sigFigCountElement.innerHTML = 'Number of Significant Figures: ' + sigFigs; var roundToSF = parseInt(roundToSigFigsStr); if (!isNaN(roundToSF) && roundToSF > 0) { var roundedVal = numVal.toPrecision(roundToSF); roundedNumberElement.innerHTML = 'Rounded Number: ' + roundedVal; } else if (roundToSigFigsStr.trim() !== ") { errorMessageElement.innerHTML = 'Please enter a valid positive integer for rounding.'; errorMessageElement.style.display = 'block'; } }

Understanding Significant Figures

Significant figures (often called sig figs or significant digits) are the digits in a number that carry meaning contributing to its precision. They are crucial in scientific and engineering fields to express the reliability of a measurement or calculation. When performing calculations, the number of significant figures in the result is often limited by the precision of the input values.

Rules for Counting Significant Figures:

  1. Non-zero digits: All non-zero digits are always significant.
    • Example: 123.45 has 5 significant figures.
    • Example: 789 has 3 significant figures.
  2. Zeros between non-zero digits (captive zeros): Zeros located between non-zero digits are significant.
    • Example: 102.05 has 5 significant figures.
    • Example: 5003 has 4 significant figures.
  3. Leading zeros: Zeros that precede all non-zero digits are NOT significant. They merely indicate the position of the decimal point.
    • Example: 0.0012 has 2 significant figures (the 1 and 2).
    • Example: 0.050 has 2 significant figures (the 5 and the trailing 0).
  4. Trailing zeros (at the end of the number):
    • With a decimal point: Trailing zeros are significant if the number contains a decimal point.
      • Example: 12.00 has 4 significant figures.
      • Example: 0.500 has 3 significant figures.
    • Without a decimal point: Trailing zeros are NOT significant unless explicitly indicated (e.g., by a bar over the last significant zero, which is not common in standard notation).
      • Example: 1200 has 2 significant figures (the 1 and 2).
      • Example: 1020 has 3 significant figures (the 1, 0, and 2).
  5. Exact numbers: Numbers that are counted or defined (e.g., 12 inches in a foot, 5 apples) have an infinite number of significant figures. This calculator focuses on measured or calculated values.
  6. The number zero: The number 0 itself is generally considered to have one significant figure.

Rounding to Significant Figures:

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

  1. Identify the desired number of significant figures.
  2. Starting from the first non-zero digit, count to the right until you reach the desired number of significant figures. This is your "last significant digit."
  3. Look at the digit immediately to the right of the last significant digit:
    • If it is 5 or greater, round up the last significant digit.
    • If it is less than 5, keep the last significant digit as it is.
  4. Replace any digits to the right of the last significant digit with zeros if they are to the left of the decimal point, or drop them if they are to the right of the decimal point, to maintain the correct magnitude of the number.

Rounding Examples:

  • Round 123.45 to 3 significant figures:
    • First 3 sig figs are 1, 2, 3. The next digit is 4 (less than 5).
    • Result: 123
  • Round 0.001234 to 2 significant figures:
    • First 2 sig figs are 1, 2. The next digit is 3 (less than 5).
    • Result: 0.0012
  • Round 98765 to 2 significant figures:
    • First 2 sig figs are 9, 8. The next digit is 7 (5 or greater). Round up 8 to 9.
    • Result: 99000 (the zeros are placeholders, not significant)
  • Round 1.2345 to 4 significant figures:
    • First 4 sig figs are 1, 2, 3, 4. The next digit is 5 (5 or greater). Round up 4 to 5.
    • Result: 1.235

Using the Calculator:

Enter your number in the "Number to Analyze" field. The calculator will automatically determine the number of significant figures based on the rules above. If you wish to round the number, enter the desired number of significant figures in the "Round to (optional) Significant Figures" field.

Note on Scientific Notation: This calculator primarily analyzes numbers in standard decimal form. While it can parse scientific notation (e.g., 1.23e-4) for its numerical value, the counting of significant figures is based on the decimal string representation you provide. For rounding, JavaScript's toPrecision() method is used, which may output results in scientific notation for very large or very small numbers, correctly preserving the specified number of significant figures.

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