Overview
This lecture explains how to identify significant figures (sig figs), apply them in calculations, and understand the scientific meanings of accuracy and precision.
Significant Figures: Counting and Identifying
- All non-zero digits in a number are significant.
- Leading zeros (zeros before non-zero digits) are never significant; they are placeholders.
- Captive zeros (zeros between non-zero digits) are always significant.
- Trailing zeros (zeros after non-zero digits) are significant only if after a decimal point.
- When in doubt, use scientific notation to clarify which digits are significant.
Significant Figures in Calculations
- The uncertainty of measurements limits the uncertainty you should report in results.
- For addition/subtraction, the answer is reported with the same number of decimal places as the measurement with the fewest decimal places.
- For multiplication/division, the answer is reported with the same number of significant figures as the measurement with the fewest significant figures.
Rounding Rules for Significant Figures
- If the dropped digit is less than 5, round down (e.g., 1.12 to 1.1 for two sig figs).
- If the dropped digit is greater than 5, round up (e.g., 4.78 to 4.8 for two sig figs).
- If the dropped digit is exactly 5, round so that the last remaining digit is even (e.g., 2.35 to 2.4 and 2.45 to 2.4).
Accuracy vs. Precision
- Accuracy is how close a measurement is to the true or accepted value.
- Precision is how close repeated measurements are to each other, regardless of the true value.
- Measurements can be: neither accurate nor precise, precise but not accurate, accurate and precise, or accurate but not precise.
Key Terms & Definitions
- Significant Figures (Sig Figs) — digits in a number that represent meaningful information about its precision.
- Leading Zero — a zero before the first non-zero digit; not significant.
- Captive Zero — a zero between non-zero digits; always significant.
- Trailing Zero — a zero at the end of a number; significant only if after a decimal.
- Accuracy — closeness of a measurement to the true value.
- Precision — closeness of repeated measurements to each other.
Action Items / Next Steps
- Practice identifying significant figures in various numbers.
- Apply the rounding rules to example problems.
- Review homework assignments or readings on measurement uncertainty.