1. Chapter 2: Analyzing Data

2. SI Units Only US and Liberia use English system
World wide, science uses SI units
Benefits of SI
Universal
Uses multiples of 10
No conversions = less error
No fractions (move decimal)
Prefixes used for all bases

3. SI Units

4. SI Units: Length and Mass
1 inch = ~2.54 cm
1 meter = ~ yard
Mass
1 kg = ~ 2.2 lbs
Measured on analytic scales in lab
Doesn’t factor gravity (therefore in space 1 kg = 0 lbs)

5. SI Units : Temperature US Fahrenheit freezing = 32 degrees
boiling = 212 degrees)
Majority World
Celsius
Freezing = 0 degrees
Boiling = 100 degrees
SI Units
Kelvin
At 0 Kelvin is where particles have lowest energy.

6. SI Units: mole Amount of a substance
1 mole of any pure element has 6.02 x 1023 atoms.
Each element has its own unique molar mass
Mass of substance
Given on periodic table

7. $620,000,000,000,000,000,000,000

8. Derived SI Units: Volume
Amount of space an object takes up
Cubes and Rectangles
Length X Width X Height
Irregular Shapes
Water displacement
1 Liter = ~ 1 quart (larger units)
1 ml = 1 cm3 (most often in lab)
29.6 ml = ~ 1 oz (12 oz can of pop has 355 ml)
Water Displacement

9. Derived SI Units: Density
Amount of mass per unit of volume
Can be used to identify substances
page 971
Objects greater density sink
Object lower density float
Mass in grams
Volume in ml or cm3

10. Scientific Notation
Science often involves numbers that are very big or very small.
Scientific notation makes the numbers easier to write

11. How wide is our universe?
210,000,000,000,000,000,000,000 miles
(22 zeros)
This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

12. Scientific Notation
A number is expressed in scientific notation when it is in the form
a x 10n
a is between 1 and 10
n is an integer.
Example: 6.02 x 1023

13. Write the width of the universe in scientific notation.
210,000,000,000,000,000,000,000 miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to make this number be between 1 and 10?
Between the 2 and the 1

14. 2.10,000,000,000,000,000,000,000.
How many decimal places did you move the decimal? 23
When the original number is more than 1, the exponent is positive.
The answer in scientific notation is
2.1 x 1023

15. 1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
9.02
The decimal was moved how many places? 8
When the original number is less than 1, the exponent is negative.
9.02 x 10-8

16. Write 28750.9 in scientific notation.
x 10-5
x 10-4
x 104
x 105

17. Practice Problems 2) Express 1.8 x 10-4 in decimal notation. 0.00018
4,580,000

18. Using a Calculator On the calculator Use or button. Example
4.58 x 106 is typed

22. 4) Use a calculator to evaluate: 4.5 x 10-5 1.6 x 10-2
Type
You must include parentheses if you don’t use buttons!!
(4.5 x ) (1.6 x )
Write in scientific notation.
x 10-3

23. 5) Use a calculator to evaluate:. 7. 2 x 10-9. 1
5) Use a calculator to evaluate: x x 102 On the calculator, the answer is:
6.E -11
The answer in scientific notation is
6 x
The answer in decimal notation is

24. 6) Use a calculator to evaluate (0. 0042)(330,000)
6) Use a calculator to evaluate (0.0042)(330,000). On the calculator, the answer is
1386.
The answer in decimal notation is
1386
The answer in scientific notation is
1.386 x 103

25. 7) Use a calculator to evaluate (3,600,000,000)(23)
7) Use a calculator to evaluate (3,600,000,000)(23). On the calculator, the answer is:
8.28 E +10
The answer in scientific notation is
8.28 x 10 10
The answer in decimal notation is
82,800,000,000

26. Write (2.8 x 103)(5.1 x 10-7) in scientific notation.

27. Write 531.42 x 105 in scientific notation.

28. Adding and Subtracting
Exponents of numbers added MUST be the SAME
If not adjust a number to make them the same
Give the answer in proper scientific notation

29. Multiplying and Dividing
Coefficients DO NOT have to be the same
2 step process
Multiplication
Multiply coefficients
Add Exponents
Division
Divide coefficients
Subtract exponent

30. Example Multiplication

31. Example Division

32. Dimensional Analysis 2.75 dozen X 12 eggs 1 dozen = 33 eggs
Used to convert from one unit to another
Allows for equivalents
Used to convert from US to SI Units
Used everyday
1 dozen eggs = how many eggs?
How many eggs in 2.75 dozen eggs?
2.75 dozen
X 12 eggs
1 dozen
= 33 eggs

33. Dimensional Analysis 1 day X 24 hour 1 day X 60 min 1 hour X 60 sec
Problem
How many seconds are in a day?
Conversion Factors
60 sec = 1min
60 min = hour
24 hours = 1day
Solve
1 day
X 24 hour
1 day
X 60 min
1 hour
X 60 sec
1 min
= 86,400 sec

34. Dimensional Analysis
Practice problem: 2.4 page 6 1) Analyze: Reread and determine specific info and data given : Determine what you need to find 2) Plan: Develop method to solve (What conversion factors do you need and how should you arrange them?) 3) Compute: Follow your plan and find answer 4) Evaluate: Make sure your answer makes sense and no errors

35. Dimensional Analysis
Practice: A car is traveling 65.0 miles per hour. How many km per hour is the car traveling? 1 mile = 5280 feet 1 inch = 2.54 cm 65.0 miles x 5280 feet x 12 inches x 2.54 cm x 1 m x 1 km = hour 1 mile 1 foot 1 inch 100 cm 1000 m = km/hr Sig figs = 105 km/hr

36. Uncertainty in Data Error always present in measurements
SI Units help prevent conversion errors only
Data results should be both…
Precise
Data repeatedly the same
Accurate
Data results measure close to actual value
Average correct

37. Uncertainty in Data and Significant Digits
Used to estimate numbers
Used in lab when collecting quantitative data
Helps provide degree of certainty

38. Rules for Significant Digits
Nonzero numbers ALWAYS significant
ex: 45,234 (5 sig figs)
Zeros between none zero numbers ALWAYS significant
ex: (5 sig figs)
Trailing zeros ONLY significant AFTER a decimal point
32,000 Not significant (2 sig figs)
Significant (4 sig figs)
Leading zeros AFTER decimal point NEVER significant
ex: (1 sig fig)

39. Significant Figures EXAMPLES 12.34 12.01 0.0032 0.3210 893,000
(4 sig figs)
12.01
0.0032
(2 sig figs)
0.3210
(3 sig figs)
893,000

40. Significant figures ON YOUR OWN 602,000 2.0156 0.00412 516.90 78,091.0
(3 sig figs)
2.0156
(5 sig figs)
516.90
78,091.0
(6 sig figs)

41. Significant Digits Rounding in Significant digits
If a 5 or greater follows round up
If the number following is 4 or less the number remains
Example:
1) Round to 3 significant digits
Answer 3.58
2) Round to 2 significant digits
Answer

42. Significant Digits On own Round 54,312.98 to 4 significant digits
54,310
Round to 3 significant digits
0.0231
Round to 3 significant digits
0.350

43. Multiplying/Dividing with Significant Digits
Find the number of significant digits in each number
Use the smaller number of significant digits in your final answer.
Example:
x .201 = 67.2

44. Multiplying/Dividing with Significant Digits
On own
x 3.1 =
2,100
9.340/3 = 3
32,000/.0342 =
940,000

45. Adding/Subtracting with Significant Digit
Must line up decimal points in numbers
Significant digits not based on total number of significant digits
Significant digits based on number of digits after decimal point
Example
1) = 48.5

46. Adding/Subtracting with Significant Digit
On own =
84.69
902 – 8.02 =
894
0.654 – =
0.561

47. Representing Data Graphs Used to determine/show patterns 3 main types
Circle/Pie charts
Bar Graphs
Line Graphs

48. Representing Data – Circle Graph
Used to show parts of a fixed whole
Bar Graph
Shows varying qualitative data
Quality measured on y-axis
Independent variable on x-axis
Line Graph
Most often used in chemistry
Represents data of independent and dependent variable
Dependent variable on y-axis

52. Representing Data- Line Graphs
Independent Variable on x-axis
Dependent variable on y-axis
Best fit lines
Not all data points exactly through all points
Line drawn to attempt to make…
equal the number of points both above and below line
If line straight…
Variables are directly related
Slope can be used to determine relationship
Slope = rise/run = ∆y/∆x
+ slope: both variables increase or both decrease
- slope: one variable increases, other variable decreases

53. What is the…
Independent Variable
Dependent Variable
What does data represent

54. Drawing a line graph
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