1. Chapter 2
Data Analysis

2. 2.1 Units of Measurement
We make measurements every day: buying products, sports activities, and cooking
Qualitative measurements are words, such as heavy or hot

3. 2.1 Units of Measurement
Quantitative measurements involve numbers (quantities) and units, and depend on:
The reliability of the measuring instrument
the care with which it is read – this is determined by YOU!
All quantitative measurements consist of two parts:
A number
A unit (the most important part of the measurement)
Examples:
20 grams
6.63 x 10-3 seconds

4. 2.1 Units of Measurement
The standards of measurement used in science are those of the Metric System, which was revised in 1960 and is now the International System of Units (SI).
Système Internationale d'Unités (SI) is an internationally agreed upon system of measurements.
A base unit is a defined unit in a system of measurement that is based on an object or event in the physical world, and is independent of other units.

5. 2.1 SI Units

6. 2.1 SI Units
The SI base unit of time is the second (s), based on the frequency of radiation given off by a cesium-133 atom.
The SI base unit for length is the meter (m), the distance light travels in a vacuum in 1/299,792,458th of a second.
The SI base unit of mass is the kilogram (kg), about 2.2 pounds. (This is the ONLY base unit with a prefix.)

7. 2.1 SI Units The SI base unit of temperature is the kelvin (K).
Zero kelvin is the point where there is virtually no particle motion or kinetic energy, also known as absolute zero.
Two other temperature scales are Celsius and Fahrenheit.

8. 2.1 Units of Temperature Fahrenheit – named after Daniel Fahrenheit
Temperature is a measure of how hot an object is (there is no such thing as cold)
Heat moves from the object at the higher temperature to the object at the lower temperature.
We use three units of temperature:
Fahrenheit – named after Daniel Fahrenheit
Celsius - named after Anders Celsius
Kelvin – named after Lord Kelvin

9. Temperature Conversions
Celsius ↔ Kelvin
Kelvin Scale – has the same temperature change increments as Celsius;
in other words, 1○C = 1 K
The difference between these scales is that the Kelvin scale has its zero point (starting point) at absolute zero.
Absolute zero is – ○C or K.

10. Note on Absolute Zero in Celsius:
Unless working with extremely low temps, convention drops the .15 so absolute zero is: –
Therefore:
○C = K – 273
K = ○C
(we do not need to write the .00 but know it is there for sig figs)

11. Ex- Temperature Conversions
What is the temp in Kelvin when the temp is ○C K = ○C K = = K What is the temp in ○C if it is K ○C = K – 273 ○C = – 273 = –37.20 ○C

12. Temperature Conversions
Celsius ↔ Fahrenheit
 ○C = (○F – 32) x 5/9
 ○F = (○C x 9/5) + 32

13. Ex- Temperature Conversions
What is the temperature in Celsius
when it is 82.65○F outside?
Subtract 32 from the temp
82.65○F – = 50.65○F
Multiply by 5/9
50.65○F x 5/9 = ○C
= ○C

14. 2.1 Other Units Not all quantities can be measured with SI base units.
A unit that is defined by a combination of base units is called a derived unit.
They are made by “doing math on it”
Speed = miles/hour (distance/time)
Density = grams/mL (mass/volume)
Sometimes, non-SI units are used
Liter, Celsius, calorie

15. 2.1 SI Units
Volume is measured in cubic meters (m3), but this is very large. A more convenient measure is the liter, or one cubic decimeter (dm3).

16. 2.1 SI Units Volume is the space occupied by any sample of matter.
Calculated for a solid by
Thus it is derived from units of length.
SI unit = cubic meter (m3)
Everyday unit = Liter (L), which is non-SI.
(Note: 1mL = 1cm3)

17. 2.1 Density Which is heavier- a pound of lead or a pound of feathers?
Most people will answer lead,
but the weight is exactly the same
They are normally thinking about equal volumes of the two
The relationship here between mass and volume is called Density

18. 2.1 Density (cont)
Density is a derived unit, g/cm3 or g/mL, the amount of mass per unit volume.
The density equation is

19. Ex – Using the Density Equation
A piece of lead has a volume of 4.34 cm3 and a mass of grams. What is the density of lead? d = m/v d = x m = g v = 4.34 cm3 d = g/cm3 d = g/cm3

20. 2.1 Units (cont)
We make use of prefixes for units larger or smaller

21. 2.1 Check Which of the following is a derived unit? A. yard B. second
C. liter
D. kilogram

22. Devices for Measuring Liquid Volume
Graduated cylinders (most common in General Chemistry)
Pipets
Burets
Volumetric Flasks
Syringes

23. Pipettes

24. Buret

25. Volumetric
Flasks

26. Syringe

27. 2.1 Check
What instruments would use to take the following measurements?
Length
Mass
Time
Temperature
Volume

28. 2.1 Check What is the relationship between mass and volume called?
A. density
B. space
C. matter
D. weight

29. 2.2 Scientific Notation
Scientific notation can be used to express any number as a number between 1 and 10 (the coefficient) multiplied by 10 raised to a power (the exponent).
Count the number of places the decimal point must be moved to give a coefficient between 1 and 10.

30. 2.2 Scientific Notation 800 = 8.0  102 0.0000343 = 3.43  10–5
The number of places moved equals the value of the exponent.
The exponent is positive when the decimal moves to the left and negative when the decimal moves to the right.
800 = 8.0  102
= 3.43  10–5

31. 2.2 Scientific Notation Addition and subtraction
Exponents must be the same.
Rewrite values with the same exponent.
Add or subtract coefficients.

32. 2.2 Scientific Notation Multiplication and division
To multiply, multiply the coefficients, then add the exponents.
To divide, divide the coefficients, then subtract the exponent of the divisor from the exponent of the dividend.

33. 2.2 Dimensional Analysis
Dimensional analysis is a systematic approach to problem solving that uses conversion factors to move, or convert, from one unit to another.
A conversion factor is a ratio of equivalent values having different units.

34. 2.2 Dimensional Analysis Writing conversion factors
Conversion factors are derived from equality relationships, such as 1 dozen eggs = 12 eggs.
Percentages can also be used as conversion factors. They relate the number of parts of one component to 100 total parts.

35. 2.2 Dimensional Analysis Using conversion factors
A conversion factor must cancel one unit and introduce a new one.

36. Example: Using the density equation
Andrew does remarkably well even in the face of some very difficult life events and a very difficult ongoing situation that he has absolutely no control over

37. 2.2 Check
What is a systematic approach to problem solving that converts from one unit to another?
A. conversion ratio
B. conversion factor
C. scientific notation
D. dimensional analysis

38. 2.2 Check
Which of the following expresses 9,640,000 in the correct scientific notation?
A  104
B  105
C × 106
D  610

39. 2.3 Accuracy and Precision
Accuracy refers to how close a measured value is to an accepted value.
Precision refers to how close a series of measurements are to one another.

40. 2.3 Accuracy and Precision

41. 2.3 Accuracy and Precision
Error is defined as the difference between and experimental value and an accepted value.

42. 2.3 Accuracy and Precision
The error equation is error = experimental value – accepted value.
Accepted value = the correct value based on reliable references
Experimental value = the value measured in the lab
Percent error expresses error as a percentage of the accepted value.

43. Why Is there Uncertainty?
Measurements are performed with instruments, and no instrument can read to an infinite number of decimal places
Which of the balances below has the greatest uncertainty in measurement?

44. Which measurement is the best?
What is the measured value?
What is the measured value?
What is the measured value?

45. 2.3 Significant Figures
Often, precision is limited by the tools available.
Significant figures include all known digits plus one estimated digit.

46. 2.3 Significant Figures Rules for significant figures
Rule 1: Nonzero numbers are always significant.
Rule 2: Zeros between nonzero numbers are always significant.
Rule 3: All final zeros to the right of the decimal are significant.
Rule 4: Placeholder zeros are not significant. To remove placeholder zeros, rewrite the number in scientific notation.
Rule 5: Counting numbers and defined constants have an infinite number of significant figures.

47. 2.3 Significant Figures
Calculators are not aware of significant figures.
Answers should not have more significant figures than the original data with the fewest figures, and should be rounded.

48. 2.3 Significant Figures Rules for rounding
Rule 1: If the digit to the right of the last significant figure is less than 5, do not change the last significant figure.
Rule 2: If the digit to the right of the last significant figure is greater than 5, round up to the last significant figure.
Rule 3: If the digits to the right of the last significant figure are a 5 followed by a nonzero digit, round up to the last significant figure.

49. 2.3 Significant Figures Rules for rounding (cont.)
Rule 4: If the digits to the right of the last significant figure are a 5 followed by a 0 or no other number at all, look at the last significant figure. If it is odd, round it up; if it is even, do not round up.

50. 2.3 Significant Figures Addition and subtraction
Round numbers so all numbers have the same number of digits to the right of the decimal.
Multiplication and division
Round the answer to the same number of significant figures as the original measurement with the fewest significant figures.

51. 2.3 Check
Determine the number of significant figures in the following: 8,200, 723.0, and 0.01.
A. 4, 4, and 3
B. 4, 3, and 3
C. 2, 3, and 1
D. 2, 4, and 1

52. 2.3 Check
Determine the number of significant figures in the following: 8,200, 723.0, and 0.01.
A. 4, 4, and 3
B. 4, 3, and 3
C. 2, 3, and 1
D. 2, 4, and 1

53. 2.3 Check
A substance has an accepted density of 2.00 g/L. You measured the density as 1.80 g/L. What is the percent error?
A g/L
B. –0.20 g/L
C g/L
D g/L

54. 2.4 Graphing
A graph is a visual display of data that makes trends easier to see than in a table.

55. 2.4 Graphing
A circle graph, or pie chart, has wedges that visually represent percentages of a fixed whole.

56. 2.4 Graphing
Bar graphs are often used to show how a quantity varies across categories.

57. 2.4 Graphing
On line graphs, independent variables are plotted on the x-axis and dependent variables are plotted on the y-axis.

58. 2.4 Graphing
If a line through the points is straight, the relationship is linear and can be analyzed further by examining the slope.

59. 2.4 Graphing
KNOW RULES FOR GOOD GRAPHING

60. 2.4 Interpreting Graphs
Interpolation is reading and estimating values falling between points on the graph.
Extrapolation is estimating values outside the points by extending the line.

61. 2.4 Interpreting Graphs
This graph shows important ozone measurements and helps the viewer visualize a trend from two different time periods.

62. 2.4 Check ____ variables are plotted on the ____-axis in a line graph.
A. independent, x
B. independent, y
C. dependent, x
D. dependent, z

63. 2.4 Check
What kind of graph shows how quantities vary across categories?
A. pie charts
B. line graphs
C. Venn diagrams
D. bar graphs

64. Ch 2 Assessment
Which of the following is the SI derived unit of volume?
A. gallon
B. quart
C. m3
D. kilogram

65. Ch 2 Assessment Which prefix means 1/10th? A. deci- B. hemi- C. kilo-
D. centi-

66. Ch 2 Assessment Divide 6.0  109 by 1.5  103. A. 4.0  106

67. Ch 2 Assessment Round the following to 3 significant figures 2.3450.B
C. 2.34
D. 2.40

68. Ch 2 Assessment
The rise divided by the run on a line graph is the ____.
A. x-axis
B. slope
C. y-axis
D. y-intercept

69. Ch 2 Assessment Which is NOT an SI base unit? A. meter B. second
C. liter
D. kelvin

70. Ch 2 Assessment Which value is NOT equivalent to the others? A. 800 m
B. 0.8 km
C. 80 dm
D. 8.0 x 105 cm

71. Ch 2 Assessment
Find the solution with the correct number of significant figures: 25  0.25
A. 6.25
B. 6.2
C. 6.3 D

72. Ch 2 Assessment
How many significant figures are there in meters?
A. 4
B. 5
C. 6
D. 11

73. Ch 2 Assessment Which is NOT a quantitative measurement of a liquid?
A. color
B. volume
C. mass
D. density