Significant Figures (Sig Figs)

Introduction

• Purpose of Measurement: To communicate experiences (distance, time, etc.).
• Units of Measurement: Some are based on natural phenomena (e.g., days, years) while others are arbitrary (e.g., lengths, masses).

Measurement Limitations

• Estimations: Avoid making estimates more precise than the measuring instrument allows.
  • Example: If a device shows 2.33 cm, do not estimate further to 2.33481 cm.

Significant Figures (Sig Figs)

• Definition: Digits in a measurement that indicate its precision.
• Estimation Rule: Estimate one digit further than the precision of the instrument.

Rules for Determining Sig Figs

1. Non-Zero Digits: Always significant (e.g., 123 has 3 sig figs).
2. Zeros Between Non-Zero Digits: Always significant (e.g., 1002 has 4 sig figs).
3. Leading Zeros: Not significant (e.g., 0.0025 has 2 sig figs).
4. Trailing Zeros: Only significant if they are decimal zeros (e.g., 100.0 has 4 sig figs).

Examples

• 10,000: Only 1 sig fig (estimation from 9,500 to 10,499).
• 10,000.0: Due to the decimal, it has more sig figs.
• 0.00450: 3 sig figs (leading zeros not significant).

Calculations with Sig Figs

• Addition/Subtraction: Answer has as many decimal places as the value with the fewest decimal places.
• Multiplication/Division: Answer has as many sig figs as the value with the fewest sig figs.
• Rounding:
  • Round up if ≥ 5.
  • Round down if < 5.

Conclusion

• Check Comprehension: Ensure understanding of the rules and application of sig figs.
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