1. Uncertainty in Measurement
Accuracy vs. Precision

2. Uncertainty Basis for significant figures
All measurements are uncertain to some degree
The last estimated digit represents the uncertainty in the measurement
Each Person may estimate a measurement differently
Person mls
Person mls
Person mls

3. Rules for Counting Significant Figures
1. Non-zeros always count as significant figures:
3456 has
4 significant figures

4. Rules for Counting Significant Figures
2. Leading zeroes do not count as significant figures:
has
3 significant figures

5. Rules for Counting Significant Figures
3. Captive zeroes always count as significant figures:
16.07 has
4 significant figures

6. Rules for Counting Significant Figures
4. Trailing zeros (or zeros after a non-zero digit) are significant only if the number contains a written decimal point:
9.300 has 4 significant figures
has 1 significant figure
100. has 3 significant figures

7. Sig Fig Practice #1 How many significant figures in the following?
5 sig figs
17.10 kg 
4 sig figs
100,890 L 
5 sig figs
These all come from some measurements
3.29 x 103 s 
3 sig figs
cm 
2 sig figs
3,200,000 mL 
2 sig figs

8. Rules for Significant Figures in Mathematical Operations
Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. =
 (3 sig figs)

9. Rules for Significant Figures in Mathematical Operations
Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation.
6.38 x 2.0 =
12.76  13 (2 sig figs)

10. Precision vs. Accuracy Precision- how repeatable
Precision is determined by the uncertainty in the instrument used to take a measurement.
So The precision of a measurement is also how many decimal places that can be recorded for a measurement.
1.476 grams has more precision than 1.5 grams.
Accuracy- how correct - closeness to true value.

11. Measurement Errors
Random error - equal chance of being high or low- addressed by averaging measurements - expected
Systematic error- same direction each time
Want to avoid this
Bad equipment or bad technique.
Better precision implies better accuracy
You can have precision without accuracy
You can’t have accuracy without precision (unless you’re really lucky).

12. Percent Error
Percent Error compares a measured value to its true value.
It measures the accuracy in your measurement.
%Error = Measured value – accepted value x 100
accepted value

13. Average Deviation
Average Deviation – measures the repeatability (or precision) of your measurements.
Deviation = measured value – average value
You calculate the deviation for each measurement and then take the average of those deviations to get the “Average Deviation”
Measurement is then reported as the average + average deviation
For example: mls mls

14. Each Person may estimate a measurement differently
Deviation
Person mls mls
Person mls mls
Person mls mls
Average mls +/ mls