Overview
This lecture covers significant figures (sig figs), their importance in measurement, the rules for identifying them, and how to use them in mathematical calculations.
Importance of Measurement and Precision
- Measurements express experiences numerically to communicate details like distance or time.
- Some units are natural (day, year), while others (length, mass) are arbitrary.
- Measurements are limited by the precision of the instrument used.
Rules for Significant Figures
- Non-zero digits are always significant.
- Zeros between non-zero digits are significant.
- Leading zeros (before the first non-zero digit) are not significant.
- Trailing zeros (after the last non-zero digit) are significant only if they are decimal zeros.
Using Significant Figures in Calculations
- For addition/subtraction, the answer has as many decimal places as the value with the fewest decimal places.
- For multiplication/division, the answer has as many significant figures as the value with the fewest significant figures.
- Round up if the next digit is 5 or higher; round down if it is 4 or below.
Examples
- "10,000" has one significant figure; it means approximately 10,000, not exactly 10,000.
- Estimations should not imply greater precision than the measurement allows (e.g., don't write 2.33481 cm when the instrument only reads 2.33 cm).
Key Terms & Definitions
- Significant Figures (Sig Figs) — digits in a measurement that reflect the precision of the measuring instrument.
- Leading Zeros — zeros before the first non-zero digit; not significant.
- Trailing Zeros — zeros after the last non-zero digit; only significant if they are decimal zeros.
Action Items / Next Steps
- Practice determining the number of significant figures in different measurements.
- Apply sig fig rules to addition, subtraction, multiplication, and division problems.