Lecture on Significant Figures

Introduction to Significant Figures

• Also known as significant digits.
• Purpose: Ensure computational results do not over-represent precision beyond the initial measurements.
• Core idea: Identify which digits convey precision of a measurement.

Identifying Significant Figures

• Example 1: 0.00700

  • Significant figures: 3 (7, 0, 0).
  • Leading zeros (0.00) are not significant; they just set scale (e.g., kilometers vs meters).
  • Trailing zeros after decimal are significant when explicitly measured (e.g., 7.00 meters).

• Example 2: 0.052

  • Significant figures: 2 (5, 2).
  • Leading zeros are not counted as significant figures.

• Example 3: 370.

  • Significant figures: 3 (3, 7, 0).
  • Decimal indicates measurement precision up to the last digit written.

• Example 4: 370.0

  • Significant figures: 4 (3, 7, 0, 0).
  • Trailing zero indicates precision to the tenth.

• Example 5: 707.010

  • Significant figures: 6 (7, 0, 7, 0, 1, 0).
  • All digits, including zeros, are significant as they are between non-zero digits.

• Example 6: 37,000

  • Ambiguous without decimal point.
  • If written without more information, likely 2 significant figures (3, 7).
  • Adding a decimal point (37,000.) clarifies precision to 5 significant figures.

Rules of Thumb for Significant Figures

• Non-zero digits are always significant.
• Leading zeros are never significant.
• Trailing zeros in a decimal number are significant.
• Zeros between non-zero digits are significant.
• Trailing zeros in a whole number without a decimal point are ambiguous and depend on additional context or notation.

Conclusion

• Significant figures are essential in accurately conveying the precision of a measurement.
• Proper notation helps reduce ambiguity in scientific measurements and calculations.