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### 1.2 Measurements in Experiments

Chapter 1 Section 2

Part 2 – Accuracy, Precision & Significant Figures

Accuracy

- Accuracy – The extent to which a reported measurement approaches the true value of the quantity measured.
- Closer to the middle of the bulls eye, the more accurate the measurement.

Precision

- Precision – The degree of exactness or refinement of a measurement.
- How close are the measurements together.

Accurate and Precise

- It is possible for objects to be both accurate and precise of none.

Accurate and Precise

Not Accurate or Precise

Significant Figures

- Significant Figures – Those digits in a measurement that are know with certainty plus the first digit that is uncertain.
- The measurement can not be more precise then the measuring device.
- Example: I can not measure inches using the odometer in a car, even though an odometer measures length.

Rules of Zeros for Sig Figs

- Zeros between other nonzero digits are significant.
- Example: 50.3 seconds (3 sig figs)
- Zeros in front of nonzero digits are not significant.
- Example: 0.0032 (2 sig figs)
- Zeros that are at the end of a number and also to the right of the decimal are significant.
- Example: 34.100 (5 sig figs)

Rules (cont.)

4. Zeros at the end of a number but to the left of a decimal are significant if they have been measured or are the first estimated digit; otherwise, they are not significant.

- Example: 1000 m (1 sig figs)

1000. m (4 sig figs)

Addition and Subtraction Rule

- The final answer should have the same number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal.

97.3

+ 5.85

103.15 → round off → 103.2

Multiplication and Division Rule

- The final answer has the same number of significant figures as the measurement having the smallest number of significant figures.

123

x 5.35

658.05 → round off → 658

Practice Problems

List how many significant figures are in each number.

- 23.56 m
- 20.044 sec
- 0.0076 hz
- 1000 kg
- 1.00000 g
- 10.40 m/s

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