1. Chapter 2
Data Analysis

2. Units of Measurement Measurement Standard Useful measurement SI Units
Comparison to a standard
Standard
Well defined
Make consistent measurements
Useful measurement
Number
Unit
SI Units
Système Internationale d’Unités—SI
Standard unit of measure

3. Units of Measurement Base units Length 7 base units (p. 26 Table 2-1)
Distance light travels through a vacuum in 1/ of a second.
Defined unit
Meter, m
Based on object or event in physical world
Mass
Defined by the platinum-iridium metal cylinder
Independent of other units
Kilogram, kg
Volume
Time
Measure of the amount of a liquid
Frequency of microwave radiation given off by cesium-133 atom
Liter, L
Second, s

4. Units of Measurement Prefixes Table p. 26
King Henry Died By Drinking Chocolate Milk
Table p. 26
Yotta (Y_): 1024
mega- micro
1 septillion
hecto (h_): 102
Yocto (y_):
deka (da_ or dk_): 10
1 septillionth
decimeter
1 dm = .1 m
10 cm = 1 dm
1000 cm3 = 1 dm3

5. Units of Measurement Derived Units
Require a combination of base units
Volume
L X W X H
1 cm3 = 1 mL = 1 cc
Density
mass/volume
DH2O = 1.00 g/mL
D = m/v
M = DV
V = M/D
Practice p. 29 #1-3; p. 30 #4-11; p. 50 #51-57

6. Units of Measurement Temperature
Measure of how hot or cold an object is relative to other objects
kelvin, K
Water
freezes about 273 K
boils about 373 K

7. Scientific Notation and Dimensional Analysis
Scientific notation expresses numbers as:
M x 10n
M is a number between 1 & 10
Ten raised to a power (exponent)
n is an integer
Adding & subtracting
Exponents must be the same
Multiplying & dividing
Multiply or divide first factors
Add exponents for multiplication
Subtract exponents for division
Practice Problems p. 32 #12-16; p. 50 #75-78

8. Scientific Notation and Dimensional Analysis
Solving problems with conversion factors
Conversion factor
Ration based on an equality
Ex. 12 in./1 ft. or 1 ft./12 in.
Ex. 7 days/1 wk
Focuses on units used
48 km =? m
(48 km)X (1000 m/1km) = 48,000 m

9. Scientific Notation and Dimensional Analysis
What is a speed of 550 m/s in km/min?
Practice Problems p. 35 #19-28; p. 51 #79-80

10. How Reliable are Measurements?
Accuracy and Precision
Accuracy
The nearness of a measurement to its accepted value
Precision
The agreement between numerical values of two or more measurements that have been made in the same way.
You can be precise without being accurate.
Systematic errors can cause results to be precise but not accurate

11. How Reliable are Measurements?
Accuracy and Precision
Percent error
Compares the size of an error to the size of the accepted value
Calculating Percent Error (Relative Error)
Percent error = error X 100
Value Accepted
Error = Value Accepted – Value Experimental
Take the absolute difference
Ignore if positive or negative integer

12. How Reliable are Measurements?
Error in Measurement
Some error or uncertainty exists in all measurement
No measurement is known to an infinite number of decimal places.
All measurements should include every digit known with certainty plus the first digit that is uncertain
Practice Problems p. 38 #29-30; p. 51 #81-82

13. How Reliable are Measurements?
Significant Figures
Represent measurements
Include digits that are known
One digit is estimated

14. How Reliable are Measurements?
Significant Figures
Rule
Examples
Non-zero numbers are always significant
72.3 g has 3
Zeros between non-zero numbers are always significant
40.7 L has 3
87009 has 5
All final zeros to the right of the decimal place are significant
6.20 g has 3
Zeros that act as placeholders are NOT significant. Convert to scientific notation.
g has 3
2000 m has 1
Constants and counting numbers have infinite number of significant figures.
6 molecules
60 s = 1 min

15. How Reliable are Measurements?
Rounding off numbers
Rule
Example
Digit to immediate right of last significant figure <5, do not change the last significant figure.
2.5322.53
Digit to immediate right of last significant figure >5, round up the last significant figure
2.5362.54
Digit to immediate right of last significant figure = 5 AND followed by a nonzero digit, round up last significant figure.
Digit to immediate right of last significant figure = 5 AND is not followed by a nonzero digit, look at last significant figure. If it is an odd digit, round it up; if it is an even digit, round it down.
2.53502.54
2.52502.52

16. How Reliable are Measurements?
Rounding off numbers
Addition and subtraction
Answer must have same number of digits to right of the decimal place as value with fewest digits to the right of the decimal point.
Example: mL mL mL
mL = 138 mL

17. How Reliable are Measurements?
Rounding off numbers
Multiplication and division
Answer must have same number of significant figures as the measurement with the fewest significant figures
Practice problems: p. 39 #31-32; p. 41 #33-36; p. 42 #37-44; p. 51 #83-85

18. Representing Data Graphing Circle graphs Bar graph
Also called pie chart
Show parts of a fixed whole, usually percents
Bar graph
Show how a quantity varies with factors
Ex. Time, location, temperature
Measured quantity on y-axis (vertical axis)
Independent variable on x-axis (horizontal axis)
Heights show how quantity varies

19. Representing Data Line Graphs
Points represent intersection of data for two variables
Independent variable on x-axis
Dependent variable on y-axis
Best fit line
Equal points above and below line
Straight line—variables directly related
Rises to the right—positive slope
Sinks to the right—negative slope
Slope = y2-y1 = Δy
x2-x Δx

20. Representing Data Interpreting Graphs
Identify independent and dependent variables
Look at ranges of data
Consider what measurements were taken
Decide if relationship is linear or nonlinear
Practice problems p #86-87