Significant Figures in Calculations

Overview

• Significant Figures (Sig Figs): Important in ensuring precision and accuracy in measurements and calculations.
• Types of Calculations:
  • Multiplication and Division
  • Addition and Subtraction

Multiplication and Division

• Rule: The result has the same number of sig figs as the measurement with the fewest sig figs.
• Key Point: The equipment with the least precision limits the accuracy of the final result.
• Example:
  • Calculation: 17.491 / 4.556
  • 17.491 has 5 sig figs; 4.556 has 4 sig figs.
  • Calculator result: 3.839113257
  • Rounded result: 3.839 (4 sig figs)
• Rounding:
  • If the next digit is 5 or above, round up.
  • If it is 4 or below, round down.
• Additional Note:
  • One sig fig measurements lead to high uncertainty.
  • Example with basic numbers: 3 x 5 = 15, rounds to 20 due to one sig fig.

Addition and Subtraction

• Rule: The result has the same number of decimal places as the measurement with the fewest decimal places.
• Example:
  • Calculation: 13.491 - 6.04
  • 13.491 has 3 decimal places; 6.04 has 2 decimal places.
  • Calculator result: 7.451
  • Rounded result: 7.45
• Visualization:
  • Draw a line after the fewest decimal places to determine where to round.
• Key Difference: Compared to multiplication/division, focus is on decimals rather than overall sig figs.

Conclusion

• Calculator Limitation: Calculators do not account for sig figs.
• Importance in Chemistry: Consistent application in calculations and lab work is crucial and affects grading.
• Practice: Further examples will be explored in class.
• Advice: Aim for more decimals to enhance precision of results.