Introduction to Significant Figures

Introduction to Significant Figures

• Significant figures are the digits in a number that convey meaningful information about the precision of a measurement or calculation.
• In other words, they indicate the reliability of a value.
• They reflect the uncertainty inherent in any measurement.

Rules for Determining Significant Figures

• Non-zero digits are always significant.
• Any zeros between two significant digits are significant.
• Leading zeros (zeros to the left of the first non-zero digit) are not significant.
• Trailing zeros in a number containing a decimal point are significant.
• Trailing zeros in a number NOT containing a decimal point are NOT significant (unless explicitly stated as significant).

Examples of Significant Figures

• 123: 3 significant figures
• 0.056: 2 significant figures
• 1000: 1 significant figure (if it is a measurement, implying uncertainty)
• 1000.: 4 significant figures (if it is intended to be precise)
• 5600: 2 significant figures (without a decimal point)
• 5600.: 4 significant figures

Rules for Calculations (Accuracy)

• For multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures in the calculation.
• For addition and subtraction, the result should have the same number of decimal places as the number with the fewest decimal places in the calculation.

Rounding Significant Figures

• If the digit to be dropped is 5 or greater, round up the preceding digit.
• If the digit to be dropped is less than 5, do not change the preceding digit.
• Example: Round 2.38 to two significant figures - the answer is 2.4.

Experimental Measurements

• Significant figures apply to all measured quantities (e.g., length, mass, volume).
• When reporting measurements, always include the appropriate number of significant figures.
• The last digit in a measurement is uncertain; the other digits are known exactly.

Importance of Significant Figures

• Accurate calculations of measurements depend on accurate recording of significant figures.
• Correct reporting of significant figures ensures results reflect the precision of instruments used in the experiment.
• Prevents misleading results from being presented.

Using Significant Figures in Scientific Notation

• Scientific notation (e.g., 2.3 x 10⁴) preserves significant figures while expressing very large or very small numbers.
• The number of significant figures is determined by the precision of the coefficient part and not by the powers of 10.

Context in Chemistry

• Chemical measurements (volume, mass, concentrations) often involve significant figures.
• Reporting results with the correct number of significant figures makes calculations more reliable.

Limitations

• Significant figures may not always reflect the true uncertainty.
• The rules for significant figures can be complex in cases involving mixed operations.
• Consistent application of these guidelines is crucial in experimental science.