Using Significant Figures

Significant Figures in Measurements

  • Purpose of Significant Figures
    • Important for reflecting the precision of measurements in scientific reporting.
    • Helps others understand the confidence in the reported value, such as the mass of an aluminum cube.

Identifying Significant Figures

  • General Rules
    • Non-zero digits are always significant.
    • Zeros between non-zero digits are significant.
    • Leading zeros (zeros to the left of the first non-zero digit) are NOT significant.
    • Trailing zeros (zeros to the right of the last non-zero digit) are significant ONLY if there’s a decimal point in the number.
Example Reporting Measurements
  1. Measurement: 0.405 grams
    • Significant Figures: 4 (0 is insignificant, the other digits are significant)
  2. Measurement: 2.00
    • Significant Figures: 3 (Zeros after the decimal are significant)
  3. Measurement: 205
    • Significant Figures: 3 (Zero is between non-zero digits, so is significant.)
  4. Measurement: 40.20
    • Significant Figures: 4 (Both zeros are significant due to the decimal point.)
Applying Significant Figures in Scientific Notation
  • Count significant figures in the coefficient (number before the power of 10).
  • The exponent does NOT affect the number of significant figures.

Rules for Calculations with Significant Figures

Multiplication and Division

  • Result should have the same number of significant figures as the value with the least significant figures.

  • Example Calculation:

    • Given: 4.6 mL (3 sig figs) and 0.78 g/mL (2 sig figs)
    • Result: Report to 2 sig figs since 0.78 g/mL has the least.
    • Calculation gives 3.588 which should be reported as 3.6 g (rounded appropriately).

  • Note about exact values:

    • Conversion factors (like 1,000 mL = 1 L) are considered exact and do not limit significant figures.
Addition and Subtraction
  • Result should have the same number of decimal places as the value with the least decimal places.
  • Example Calculation:
    • For 3.7 mL (1 decimal) and any other number involved, report the result with 1 decimal.

Practice with Calculated Results

  • Example 1: Subtraction

    • Calculate: 5.0 ATM - 0.3 ATM
    • Reported answer: 4.5 ATM (rounded to 1 decimal, matching 0.3 ATM).

  • Example 2: Division

    • Calculate: 504 g / 60.0 mL
    • Reported answer: 8.62 mol (3 sig figs from 504 g).

Conclusion

  • Familiarity with recognizing and applying significant figure rules is crucial for accurate scientific communication.
  • They reflect the precision of measurements and should seamlessly carry through any calculations.