Lecture on Significant Figures (Sig Figs)

Introduction

• Importance of communication in measurements
  • Examples: distance between cities, timing of events
• Development of measurement units
  • Natural units: day, year (based on Earth's motion)
  • Arbitrary units: many units of length and mass

Measurement Limitations

• Be aware of precision limitations
  • Example: Estimating crowd size (10,000 vs 10,472)
• Use of measuring devices
  • Only estimate one digit further than the precision of the instrument
  • Example: Estimate 2.33 cm, not 2.33481 cm

Significant Figures (Sig Figs)

• Sig Figs indicate the precision of a measurement

Rules for Determining Sig Figs

1. Any non-zero digit is significant
2. Zeros between non-zero digits are significant
3. Leading zeros are not significant
4. Trailing zeros are significant only if they are decimal zeros
   • Example: 10,000 has one significant figure (approximately 10,000)

Estimation and Rounding

• Estimations based on sig figs
  • Example: Crowd estimation from 9,500 to 10,499 rounds to 10,000

Calculations with Sig Figs

• Addition/Subtraction
  • Result has as many decimal places as the least precise measurement
• Multiplication/Division
  • Result has as many sig figs as the measurement with the least sig figs
• Rounding rules
  • 5 or higher: round up
  • 4 or below: round down

Conclusion

• Importance of understanding and applying significant figures in scientific calculations
• Encouragement to subscribe and reach out for more tutorials