1. Ch1 Measurements and Uncertainties
Pei Yi Wu

2. A clever way to estimate enormous numbers - Michael Mitchell

3. Scientific Notation

4. Calculating with Scientific Notation
Adding and Subtracting 1.40 x x 105
Change the power of ten to the same, then add
=1.75 x 106
Multiplication 3.5 x 105 x 2.0 x 108
Multiply, add powers
=7.0 x 1013
Division 4.5 x 105 x 3.0 x 102
Divide, subtract powers
=1.5 x 103

5. Concept Question
7.5x106 / 3.0x102
1.2x103 x 3.0x102
4.0 x x103

6. Precision vs. Accuracy
Precision is reproducibility of experimental data, to a certain digit placeholder. Your result can only be as precise as your worse instrument.
Accuracy is how close results are to currently accepted values by the scientific community (if there is one)

7. Significant Figures

8. Concept Question How many significant figures? (sig. figs.)
200
202
200.00
200.02
0.02
0.002

9. Concept Question Read the following measurements to the correct number of 1)significant digits 2)uncertainty

10. Uncertainties in Measurement
Systematic Errors – zero errors. Instruments have to be frequently recalibrated against a standard.
Random Errors
Parallax errors – occurs when reading an instrument not directly overhead#
A fluctuating last digit in a sensitive instrument
Time errors – human reflex ± 0.1 s

11. % Error (Relative Error)
Normalizes error against standard.
For ex. 5cm error for a 10cm measurement vs. a 100cm measurement.

12. Practice Time Precision vs. Accuracy, % Error WS

14. Metric Multipliers (Prefixes)

15. Fundamental vs. Derived Units
Level 1 m a
Level 2 F= ma
Level 3 E = F*x
Level 4 P = E/t

16. Symbols in the Greek Alphabet

17. Unit Conversions (Dimensional Analysis)
Conversion Factor – a pair of measurements with different units that is equal
Conversion factors can be freely flipped
There can be 2 story conversions

18. Creative Use of Dimensional Analysis
To be sure you solved correctly
To solve in case you don’t remember the equation….
 For example, you don’t remember the formula to solve for Power,
but you know the units of power to be Watts

19. Practice Time Dimensional Analysis and Conversion Factors

20. Propagation of Uncertainties Add. Subtrct.

21. Propagation of Uncertainties Mult. Div.

22. Propagation of Uncertainties Powers

23. Linearizing Graphs

26. Vectors and Scalars
Vector Math