1. Measurement, Error, & Uncertainty
Overview
Units in chemistry
Graphs
Scientific notation & Orders of Magnitude
Error and Significant Figures

2. Units Metric system: SI = Système Internationale Length: meters (m)
centimeters (cm) 100 cm = 1 m
Millimeters (mm) 1000 mm = 1 m
Kilometers (km) m = 1 km
Temperature:
Kelvin (K) = oC

3. Units Mass Grams (g) Milligrams (mg) 1000 mg = 1 g
Kilograms (kg) 1000 g = 1 kg
Volume
Liters (L)
Milliliters (mL) 1000 mL = 1 L
Time
Sec (s)

4. Problem 1 Express the following in the units indicated: 558 m in km
g in mg
116,322 mL in L
kg in g, in mg

5. Problem 1 1000 km·m = 558 m·x km 558 m in km 1000 m = 1 km 558. m
b) g in mg
1000 mg = 1 g
= 8.94 mg

6. Problem 1 c) 116,322 mL in L 1000 mL = 1 L 116,322 mL = 116.322 L
d) kg in g, in mg
1000 g = 1 kg
kg = 8.89 g = mg

7. Graphs
Reading graphs

8. Reading Graphs

9. Ozone Levels
Problem 2
What time of day are ozone levels at their lowest?
What time of day are ozone levels at their highest?
If levels > 84 ppb are considered harmful, what percentage of the day has levels above “harmful”?

10. Rationale for Graphing
Mass (g)
Volume (mL)
2.334
1.63
5.743
4.02
9.944
6.96
7.002
4.90
Power of the visual depiction of data to understand relationships

11. Scientific Notation Used to express very large or very small numbers:
55,800,000 km from earth to sun:
5.58 x 107 km
Mass of a H atom: g
1.68 x 10–24 g

12. Problem 3 Put the following numbers into scientific notation
346,000,000,000
340

13. Problem 3
346,000,000,000 = 3.46 x 1011
= x 10–4
= x 10–9
340 = 3.4 x 102

14. Significant Figures and Error
E.g. Density calculation:
22 g has volume of 19 mL
Density = g/mL
Not truthful value
Precision vs. Accuracy

15. Precision vs. Accuracy
Precision: depends upon the detection limit or “sensitivity” of the instrument used
Accuracy: Difference between the “true value” and the average of a series of measurements
True values rarely known: need multiple, repetitive measurements

16. Precision vs. Accuracy

17. Types of “Error”
Every scientific measurement has error associated with it
Error implies mistake: uncertainty better way to look at it
Random (indeterminate) error: result from large number of minute variations in materials, conditions, equipment, etc.; completely unavoidable. Can be (never eliminated) mitigated by improving precision, calibration
Systematic (determinate) error: result of inaccurate calibration, sampling or procedural bias, operator error, etc. Measurements are systematically low or high. Only error that we can eliminate

18. Precision vs. Accuracy
bias
bias

19. Back to Significant Figures
Place holders: not significant
Actual values or illustrating precision: significant
E.g.:
45,600 vs. 45,600.0 vs
Scientific notation solves issue
2.34 x 10–4 compared to x 10–4

20. Full Disclosure Significant figures: crude approach
Standard deviation (statistics) more appropriate
Error values (error bars on graphs)
3.44 mL  0.04 mL implies range 3.40 – 3.48 mL
If error were  0.1, could only report 3.4  0.1

21. Error Bars