Overview
This lecture covers the definitions and differences between precision and accuracy, methods of taking measurements, and rules for determining significant figures (sigfigs) in scientific data.
Precision vs. Accuracy
- Precision describes how close a series of measurements are to each other.
- Accuracy is how close a measurement is to the accepted or true value.
- Measurements can be precise but not accurate, accurate but not precise, both, or neither.
Measuring with a Ruler
- Always add one estimated digit beyond the smallest marking on the ruler.
- Estimate one place smaller than the smallest graduation on the ruler.
- If a measurement falls exactly on a line, add a zero in the next decimal place as the estimated digit.
Levels of Measurement Precision
- If each line is 10 cm, estimate to one's place (e.g., 6 or 7).
- If each line is 1 cm, estimate to the tenths place (e.g., 6.7 or 6.8).
- If each line is 0.1 cm, estimate to the hundredths place (e.g., 6.75 or 6.70).
Significant Figures (Sigfigs)
- Sigfigs include all the known digits plus one estimated digit.
- More digits (e.g., 6.70 vs. 6.7) indicate a more precise measurement.
Rules for Counting Significant Figures
- All nonzero digits are significant.
- Captive zeros (between nonzero digits) are significant.
- Trailing zeros are significant only if a decimal point is present.
- Trailing zeros are not significant if no decimal point is present.
- Leading zeros (before nonzero digits) are never significant.
Atlantic and Pacific Rule for Sigfigs
- Atlantic Rule: If decimal is absent (A for Atlantic, A for Absent), count sigfigs from the right after skipping zeros.
- Pacific Rule: If decimal is present (P for Pacific, P for Present), count sigfigs from the left after skipping zeros.
- For both rules, count all digits after the first nonzero digit.
Key Terms & Definitions
- Precision — closeness of repeated measurements to each other.
- Accuracy — closeness of a measurement to the accepted value.
- Estimated digit — last digit in a measurement, representing uncertainty.
- Significant figures (sigfigs) — digits in a measurement known with certainty plus one estimated digit.
- Captive zeros — zeros between nonzero digits, always significant.
- Trailing zeros — zeros at the end of a number; significance depends on presence of a decimal.
- Leading zeros — zeros before the first nonzero digit, never significant.
Action Items / Next Steps
- Review the rules for significant figures and practice applying the Atlantic and Pacific rules.
- Practice measuring objects and recording proper significant figures.
- Rewatch the video or consult your instructor if further clarification is needed.