1. Data Analysis
Chapter 2

2. Our Goals Learn: Units of measure: Lb, sec, acre, hours….
How to convert units:
Seconds to years
Very big and very small numbers
Which numbers matter

3. Too many units Mass: Lb, gram, ounce Temp oF,oC,K Length in, cm Time:
Sec, hr

4. The official units: SI units
Quantity
Unit
Time
Second (s)
Length
Meter (m)
Mass
Kilogram (kg)
Temperature
Kelvin (K)
Amount of substance
Mole (mol)
Electric current
Ampere (A)
Luminous intensity
Candela (cd)

5. Close your notebooks Quantity Unit Time Second (s) Length Meter (m)
Mass
Kilogram (kg)
Temperature
Kelvin (K)
Amount of substance
Mole (mol)
Electric current
Ampere (A)
Luminous intensity
Candela (cd)

6. Prefixes
Gram
1 g
Kilogram
1000 g
Milligram
0.001 g

7. Prefixes Prefix Symbol Factor Sci. Not. Ex. Giga G 109 Gigameter (Gm)
1,000,000,000
109
Gigameter (Gm)
Mega M
1,000,000
106
Megagram (Mg)
Kilo k
1,000
103
Kilometer (km)
Deci d
1/10
10-1
Deciliter (dL)
Centi c
1/100
10-2
Centimeter (cm)
Milli c
1/1,000
10-3
Milligram (mg)
Micro m
1/1,000,000
10-6
Microgram (mg)
Nano n
1/1,000,000,000
10-9
Nanometer (nm)
Pico p
1/1,000,000,000,000
10-12
Picometer (pm)

8. Prefixes: Close your notebooks
Symbol
Factor
Sci. Not.
Ex.
Giga G
1,000,000,000
109
Gig meter (Gm)
Mega M
1,000,000
106
Mega gram (Mg)
Kilo k
1,000
103
Kilometer (km)
Deci d
1/10
10-1
Deciliter (dL)
Centi c
1/100
10-2
Centimeter (cm)
Milli c
1/1,000
10-3
Milligram (mg)
Micro m
1/1,000,000
10-6
Microgram (mg)
Nano n
1/1,000,000,000
10-9
Nanometer (nm)
Pico p
1/1,000,000,000,000
10-12
Pico meter (pm)

9. 3 Derived Units Speed Meters per second m/s Density g/mL Mass/volume
More soon
Volume
cm3
1 cm3 = 1 mL

10. How many cubic centimeters are in one liter?
1L = 1000 mL = 1000 cm3
(= 10 cm x 10 cm x 10 cm)

11. Density: our first formula

12. 13.5 g of aluminum has a volume of 5 mL. Density?

13. What is the mass of 2 mL of aluminum?
d =m/v
v = 2 mL
Density = 3.7 g/mL
Must rearrange formula…

14. d = m/v m =? Rearranging formulas- 3 ways
1. pure math
d = m/v
Multiply both sides by v
dv =mv/v
cancel out like terms
dv =m

15. d = m/v m =? Rearranging formulas- 3 ways
2. replace with numbers
d = m/v
4 = 8/2
8 = 4 x 2
m = dv

16. d = m/v m =? Rearranging formulas- 3 ways
3. the triangle method
d =?
m/v
v = ?
m/d
m = ? vd
divide m v d
multiply

17. What is the mass of 2 mL of aluminum?
d =m/v
m = vd
v = 2 mL
d = 2.7 g/mL
m = (2 mL)(2.7 g/mL)
= 5.4 g

18. Reality check Each mL weighs 2.7 g We have 2 of them (2 mL)
What is the mass of 2 mL of aluminum?
Each mL weighs 2.7 g
We have 2 of them (2 mL)
Weight should be 5.4 g

19. Solving problems
Find a formula
Rearrange
Plug in
Do a reality check.

20. Kelvin (our second formula)
Temp scale that cannot go below zero
K = oC +273

21. 25oC = ?K
K = oC +273
= 300 K

22. K, oC, and oF

23. Scientific Notation

24. What it’s for: Mass of earth = 5,974,200,000,000,000,000,000,000 kg
Mass of electron = , kg
wowowowow!

25. Positive Exponents 101 = 10 102 = 10X10= 100 103 = 10X10X10 = 1000
104 =
10X10X10X10 = 10,000

26. Negative Exponents 10-1 = 1/10 = 0.1 10-2 = 1/100 = 0.01 10-3 =
1/1000 = 0.001
10-4 =
1/10000 =

27. Scientific Notation: big numbers
10,000 = 1 X 104
250,000 =
2.5 X 105
Count places to the left until there is one number to the left of the decimal point.
Always 10x
Always 1-10

28. Try some
200 =
2.00 x 102
210 =
2.10 x 102
9742=
9.742 x 103
318746=
x 105

29. Scientific Notation: small numbers=
6 X 10-5 =
4.5 X 10-4
Count places to the right until there is one number to the right of the decimal point
0.003 =
3 x 10-3
= ?
2.5 x 10-6

30. Now lets go back:
Mass of earth = 5,974,200,000,000,000,000,000,000 kg =?
x 1024 kg
Mass of electron = kg = ?
x kg
better!

31. Multiplying with Scientific Notation
Add the Exponents
102 X 103 = 105
100 X 1000 = 100,000

32. Multiplying with Scientific Notation: no calculators
(2 X 102)(3 X 103)
Multiply the Coefficients
2 X 3 = 6
Add the Exponents
102 X 103 = 105
6 x 105
60,000

33. Watch out- (2 x 103)(6 x 105) = ? Answer: = 12 x 108 No! must be 1-10
= 1.2 x ”right-down, left up”
Add: = 8
Multiply: =12

34. QUESTIONS
IF YOU DON’T ASK I CAN”T HELP YOU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
ASK NOW OR FOREVER HOLD YOUR PEACE>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

35. Using the Exponent Key on a Calculator

36. EE or EXP means “times 10 to the…”
How to type out 6.02 x 1023: 6 EE . 3 2 6 EE . 3 2
Don’t do it like this…
wrong! 6
y x . 3 2
wrong!
…or like this… x 1 6 . 2 EE 3
…or like this:
too much work.
y x 3 2 x 1 6 .

37. Also, know when to hit your (–) sign…
…before the number,
…after the number,
…or either one.

38. Example:
1.2 x 105
2.8 x 1013 = 1 . 2 EE 5 3 8
Type this calculation in like this:
–09
Calculator gives…
E–09
or…
This is NOT written…
4.3–9
4.3 x 10–9
4.3 E –9 or
But instead is written…

39. No calculators 6 x 102 /3 x 101 = ? Answer: 2 x 101 Divide: 6/3 = 2
Reality check: 600/30 = 20
Subtract: 2-1 = 1

40. Try some:

41. I have 24 eggs. How many dozen eggs do I have? 2 dozen
Unit Conversion
I have 24 eggs. How many dozen eggs do I have?
2 dozen
Why was that so easy?

42. Equalities length 10.0 in. 25.4 cm 12 eggs = 1 dozen eggs

43. Learning Check 1. 1000 m = 1 ___ a) mm b) km c) dm
g = 1 ___ a) mg b) kg c) dg
L = 1 ___ a) mL b) cL c) dL
m = 1 ___ a) mm b) cm c) dm

44. Conversion Factors are equalities
Example: in. = 2.54 cm
Factors: 1 in and cm
2.54 cm in.

45. How many minutes are in 2.5 hours?
Find a conversion factor:
60 minutes = 1 hour
Set up your equation so units cancel:
Hours cancel

46. Sample Problem
You have $7.25 in your pocket in quarters. How many quarters do you have?
7.25 dollars quarters
1 dollar
= 29 quarters X

47. Learning Check
Write conversion factors that relate each of the following pairs of units:
1. Liters and mL
2. Hours and minutes
3. Meters and kilometers

48. Learning Check a) 2440 cm b) 244 cm c) 24.4 cm
A rattlesnake is 2.44 m long. How long is the snake in cm?
a) cm
b) 244 cm
c) 24.4 cm

49. How many seconds are in 1.4 days? Unit plan: days hr min seconds
Learning Check
How many seconds are in 1.4 days?
Unit plan: days hr min seconds
1.4 days x 24 hr x ??
1 day

50. Solution Unit plan: days hr min seconds
1.4 day x 24 hr x 60 min x 60 sec
1 day hr min
= 1.2 x 105 sec

51. Wait a minute! What is wrong with the following setup?
1.4 day x 1 day x min x 60 sec
24 hr hr min
Doesn’t cancel!

52. English and Metric Conversions
If you know ONE conversion for each type of measurement, you can convert anything!
513 only: You must memorize and use these conversions:
Mass: 454 grams = 1 pound
Length: cm = 1 inch
Volume: L = 1 quart

53. Learning Check
An adult human has 4.65 L of blood. How many gallons of blood is that?
Unit plan: L qt gallon
Equalities: 1 quart = L
1 gallon = 4 quarts
Your Setup:

54. Steps to Problem Solving
Read problem
Identify data
Make a unit plan from the initial unit to the desired unit
Select conversion factors
Change initial unit to desired unit
Cancel units and check
Do math on calculator
Give an answer using significant figures

55. Dealing with Two Units – Honors Only
If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of feet?

56. Solution Initial 8450 ft x 12 in. x 2.54 cm x 1 m 1 ft 1 in. 100 cm
x 1 min x 60 sec = sec
65 m min

57. What about Square and Cubic units? – Honors Only
Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also!
Best way: Square or cube the ENITRE conversion factor
Example: Convert 4.3 cm3 to mm3
10 mm = 1 cm;
(10 mm)3 = (1 cm)3;
103 mm3 = 13 cm3;
1000 mm3 = 1 cm3
note 10 mm3 is not equal to 1 cm3
4.3 cm mm3
1 cm3
= 4300 mm3

58. Learning Check
A Nalgene water bottle holds 1000 cm3 of dihydrogen monoxide (DHMO). How many cubic decimeters is that?

59. So, a dm3 is the same as a Liter ! A cm3 is the same as a milliliter.
Solution
( )
1000 cm dm 3
10 cm
= 1 dm3
So, a dm3 is the same as a Liter !
A cm3 is the same as a milliliter.

60. Percent Error

61. Calculating Percent Error
Calculate the percent errors for each trial. Report your answers to two places after the decimal point.

62. Calculating Percent Error
Data Analysis: Additional Concepts
Topic 3
Calculating Percent Error
Substitute each error into the percent error equation. Ignore the plus and minus signs. Note that the units for density cancel out.

63. Significant Figures

64. Significant Figures
The numbers reported in a measurement are limited by the measuring tool
Significant figures in a measurement include the known digits plus one estimated digit

65. Counting Significant Figures
RULE 1. Non-zero digits are always significant.
Number of Significant Figures
38.15 cm
5.6 ft
65.6 lb ___
m ___ 4 2 3 5

66. Leading Zeros
RULE 2. Leading zeros in decimal numbers are NOT significant.
Number of Significant Figures
0.008 mm 1
oz 3
lb ____
mL ____ 2 3

67. Sandwiched Zeros RULE 3. In-between zeros are significant. 50.8 mm 3
Number of Significant Figures
50.8 mm 3
2001 min 4
0.702 lb ____
m ____ 3 3

68. Trailing Zeros 25,000 in. 2 200. yr 1, 2, 3 48,600 gal ____
RULE 4. Trailing zeros in numbers without decimals are NOT significant. Trailing zeros with decimals ARE significant
Number of Significant Figures
25,000 in. 2
200. yr 1, 2, 3
48,600 gal ____
25,005,0.00 g ____ 3 8

69. Learning Check
A. Which answers contain 3 significant figures?
1) ) ) 4760
B. All the zeros are significant in
1) ) ) x 103
C. 534,675 rounded to 3 significant figures is
1) ) 535, ) 5.35 x 105

70. Learning Check 2) 400.0 and 40 3) 0.000015 and 150,000
In which set(s) do both numbers contain the same number of significant figures?
1) and 22.00
2) and 40
3) and 150,000

71. Learning Check
State the number of significant figures in each of the following:
A m
B L
C g
D m
E. 2,080,000 bees

72. Significant Numbers in Calculations- please don’t write
A calculated answer cannot be more precise than the measuring tool.
A calculated answer must match the least precise measurement.
Significant figures are needed for final answers from
1) adding or subtracting
2) multiplying or dividing

73. Adding and Subtracting
The answer has the same number of decimal places as the measurement with the fewest decimal places.
one decimal place
two decimal places
answer??
answer one decimal place

74. Learning Check
In each calculation, round the answer to the correct number of significant figures.
A =
1) ) ) 257
B =
1) ) ) 40.7

75. Multiplying and Dividing
maintain the fewest significant figures in your answer.

76. Learning Check A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 =
1) ) )
B ÷ =
1) ) ) 60
C X =
X 0.060
1) ) )

77. Reading a Meterstick
. l I I I I cm
First digit (known) = ?? cm
Second digit (known) = ? cm
Third digit (estimated) between
Length reported = cm
or cm
or cm

78. Known + Estimated Digits
In 2.76 cm…
Known digits 2 and 7 are 100% certain
The third digit 6 is estimated (uncertain)
In the reported length, all three digits (2.76 cm) are significant including the estimated one

79. Learning Check . l8. . . . I . . . . I9. . . .I . . . . I10. . cm
What is the length of the line?
1) cm
2) cm
3) cm
How does your answer compare with your neighbor’s answer? Why or why not?

80. Zero as a Measured Number
. l I I I I cm
What is the length of the line?
First digit ?? cm
Second digit ? cm
Last (estimated) digit is cm

81. End chapter 2 