Chemisrty 106: sig figs and accurancy and preciese 1/28/2026

Context of Measurement: The speaker discusses personal experiences related to inaccurate height measurements taken during medical visits.
- Last measured height at doctor's office: 6'1" (discrepancy noted).
- Typical measured height: 6'0" and 1/8".
- Claims significance of measurement uncertainty, emphasizing inconsistency across medical facilities.

Application in Critical Situations: In contexts like chemotherapy, precise measurements are crucial.
- Example: Dosage of a chemotherapy drug must be correctly measured (e.g., 200 milligrams).
- A dosage mistake (e.g., 800 milligrams) can result in fatal outcomes.
Stakes in Measurement: The implications of measurement uncertainty vary; some situations require high precision while others do not.

Key Concepts: No measured quantity can be deemed perfect; discussions about measurement accuracy and relevance are prevalent among scientists.
Terms Introduced: Accuracy and precision will be defined to convey how measurements convey certainty.

Definition of Accuracy: Refers to how close a measured value is to the true or actual value.
- Example: Personal height measurement reflects knowledge of true height being around 6 feet.

Definition of Precision: Concerns the repeatability of measurements; how close repeated measurements of the same quantity are to each other.
- Distinction from accuracy: A measurement can be precise but not accurate, and vice versa.
- Requires multiple measurements to assess.

Independence: Measurements can exhibit one without the other.
- Accurate but not precise: Measurements are around the true value but scattered.
- Precise but not accurate: Measurements cluster together but are far from the true value.
- Ideal condition: Measurements should be both accurate and precise.

Graphical Representation: Describes accuracy and precision using a dartboard analogy, visualizing different outcomes for various dart throwers:
- First Thrower: Precise but not accurate (darts cluster but away from the center).
- Second Thrower: Accurate but not precise (darts spread around the center).
- Third Thrower: Neither accurate nor precise (darts far from center and spread).
- Fourth Thrower: Both accurate and precise (all darts clustered around the true center).

Setup: Three chemists weigh a standardized mass of 10 grams:
- First chemist: Measures 9.98g, 9.97g, 10.01g (high precision and accuracy).
- Second chemist: Measures 9.90g, 10.12g, 10.01g (accurate average but imprecise).
- Third chemist: Measures 9.46g, 9.50g, 9.48g (neither accurate nor precise).

Definition of Sig Figs: They summarize the precision of a measurement, indicating how confident we are in numbers.
Example of Height Measurement: Communicating height as, "6 feet" is less precise than, "6 feet and 5/16 inches."
Precision Indicator: More significant figures indicate greater precision.

Non-zero digits are always significant.
- Example: In 345, all digits are significant (3 sig figs).
Zeros between non-zeros are significant.
- Example: In 1,002, the zeros are significant (4 sig figs).
Leading zeros (preceding non-zero digits) are not significant.
- Example: 0.001002 has 4 sig figs.
Trailing zeros (following a decimal) are significant.
- Example: 2.50 has 3 sig figs.
Ambiguity of trailing zeros before a decimal:
- Example: 250 can have 2 or 3 sig figs; better expressed in scientific notation.

Recommendation: To avoid ambiguity, numbers should be expressed in scientific notation.
- Example: 250 grams can be expressed as 2.50 x 10^2 or 2.5 x 10^2 depending on the number of sig figs intended.
Measurement Tools Limitations: Broader discussion about how precise measurements depend on the measuring instrument used; better instruments yield more significant figures leading to greater measurement confidence.

Assignment: Practice using significant figures on newly presented examples for the next class.
Importance of recognizing the implications of measurement accuracy and precision in both science and daily life.