Overview
This lecture explains the concept of significant figures (sig figs), their importance in measurement, and the rules for counting and rounding them during calculations.
Importance of Significant Figures
- Significant figures indicate the precision of a measurement.
- Measurement is limited by the precision of the instrument being used.
- Estimates should not exceed the capabilities of the measuring device.
Rules for Counting Significant Figures
- All non-zero digits are 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 after a decimal point.
Applying Significant Figures in Calculations
- For addition or subtraction: the result has as many decimal places as the number with the fewest decimal places.
- For multiplication or division: the result has as many significant figures as the value with the fewest sig figs.
- When rounding, 5 or higher rounds up; 4 or below rounds down.
Key Terms & Definitions
- Significant figures (sig figs) — digits in a number that reflect the precision of a measurement.
- Leading zeros — zeros before the first non-zero digit; not significant.
- Trailing zeros — zeros after the last non-zero digit; only significant if they follow a decimal point.
Action Items / Next Steps
- Practice identifying significant figures in various measurements.
- Apply sig fig rules to sample addition, subtraction, multiplication, and division problems.