1. 2.1 – Data Analysis Objectives:
Differentiate between SI base and derived units
Identify appropriate SI units for various measurements
Convert between common SI prefixes (change magnitudes)
Describe the Celsius and Kelvin temperature scales

2. 2.1 – Units of Measurement Systeme International d’Units (SI System)
‘The Metric System’
Uses 7 ‘Base Units’ to measure everything that can be measured
Base units reflect some natural constant condition (except kg)
Rules of usage
An abbreviated metric unit is referred to as a ‘symbol’.
Symbols are never followed by a period unless they end a sentence.
Symbols should only follow numbers – they’re not abbreviations.
Leave a space between the number and the symbol.
Symbols are always written in the singular – no ‘s’ to make it plural.
Never use ‘p’ in an SI symbol to indicate ‘per’ (as in mph)– use a ‘/’
Capitalization matters – be careful.
SI units named after people are not capitalized, but the symbol is.

3. 2.1 – Units of Measurement Systeme International d’Units (SI System)
The Base Units
Quantity
Unit
Symbol
Length
meter m
Mass
kilogram kg
Time
second s
Electric current
ampere A
Temperature
kelvin K
Amount of substance
mole
mol
Luminous intensity
candela cd

4. 2.1 – Units of Measurement Systeme International d’Units (SI System)
Derived Units
Units of measure made by combining the seven base units.

5. 2.1 – Units of Measurement Systeme International d’Units (SI System)
Changing Magnitude - Prefixes
Prefix
Symbol
Multiplier
giga- G-
mega- M-
kilo- k-
1000
hecto- h-
100
deka-
da- 10
unit 1
deci- d-
1/10
centi- c-
1/100
milli- m-
1/1000
micro- μ-
1 /
nano- n- 1/
Move the decimal place to the right
Move the decimal place to the left

6. 2.1 – Units of Measurement Systeme International d’Units (SI System)
Changing Magnitude - Prefixes
0.001
kilo- k-
0.1
deka-
da-
0.01
hecto- h-
1.0
unit 10
deci- d-
100
centi- c-
1000
milli- m-
King Henry DAngled Under Dirty Capuchin Monkeys
King Henry Doesn’t Usually Drink Chocolate Milk

7. 2.1 – Units of Measurement Useful Non-SI Units in Chemistry Liters (L)
1 liter (L) = 1 dm3
1 milliliter (mL) = 1 cm3
1 kiloliter = 1 m3
Celsius (oC)
0 oC = freezing point of pure water at standard pressure
100 oC = boiling point of pure water at standard pressure
The Kelvin scale (K) is much better, because there are no negative temperatures, but the Celsius scale is still useful.
0 K = ‘absolute zero’ = -273 oC
0oC = 273 K and 100oC = 373 K
Kelvins and oC are the same size, just offset by 273

8. 2.2 – Scientific Notation Objectives:
Convert between scientific notation and standard form
Use scientific notation correctly with your calculator
Solve chemistry calculations using an ordered process
Follow units through a calculation
Use dimensional analysis to convert between units

9. 2.2 – Scientific Notation Scientific Notation 1 – 9.99 x 10x Used
For expressing very large or very small numbers
For expressing level of precision (significance)
Uses numbers (significant or coefficient) from 1 – 9.99 and a multiplier (exponent) to show order of magnitude.
1 – 9.99 x 10x
Positive exponents are used to show values greater than 1.
850
= 8.5 x 10 x 10
= 8.5 x 102
8500.
= x 10 x 10 x 10
= x 103
4321
= x 10 x 10 x 10
= x 103
= x 10 x 10 x 10 x 10 x 10 x 10
= x 106
Negative exponents are used to show values less than 1.
0.0023
= 2.3  10  10  10
= 2.3 x 10-3
= 2.3  10  10  10  10  10
= 2.3 x 10-5

10. 2.2 – Scientific Notation Scientific Notation 6.02 x 1023 =
Samples
Put in standard form.
1.87 x 10–5 =
3.7 x 108 =
7.88 x 101 = 78.8
2.164 x 10–2 =
Change to scientific notation.
= x 104
= 3.69 x 10–1
= 8 x 10–3
= 1 x 109
6.02 x 1023 =

11. These calculators all show the same number 6.02 x 1023.
2.2 – Scientific Notation
Scientific Notation
Using your calculator
Using scientific notation can cause problems with the order of mathematical operations.
Every calculator has a method to enter scientific notation as a single expression so you don’t need ( ).
Never use “^”!
These calculators all show the same number 6.02 x 1023.

12. 2.2 – Scientific Calculations
Chemistry Math
Follow the same steps every time!!
List the data values given with their correct variable.
List the response variable (the variable you are solving for)
Select the correct formula.
Isolate the response variable
Substitute the values and solve.
Find the mass of an object with a density of 5 g/mL and a volume of 10 mL.
m = ?
ρ = 5 g/mL
V = 10 mL
ρ = m/V
(V) ρ = m/V (V)
V ρ = m
10 mL  5 g/mL = m
50 g = m

13. 2.2 – Scientific Calculations
Chemistry Math
Isolating Variables
A key step in solving chemistry problems is isolating a variable of interest.
The solution of a given equation does not change if we:  
Add or subtract the same number from both sides of the equation
Solve for x, x + y = z
-y + x + y = z – y
x = z – y
Solve for x, x - y = z
+y + x - y = z + y
x = z + y

14. 2.2 – Scientific Calculations
Chemistry Math
Isolating Variables
The solution of a given equation does not change if we:  
Multiply both the sides with the same number or divide both the sides with the same non-zero number.
Solve for x, xy = z
xy = z
x = z x
Solve for x,
= z y y y x y
= z
(y) x y y y
= z
(y) y
x = zy

15. 2.2 – Scientific Calculations
Chemistry Math
Dealing with Units
Units must always be carried through the calculation into the answer:
5.2 kg (2.9 m)
(18 s)(1.3 s) =
kg•m s2
0.64
4.8 kg (23 s)
(18 s)(37 s) = kg s
0.57

16. 2.2 – Data Analysis Dimensional Analysis Converting Units
Method of converting units using equivalent measures
Conversion factors
Any two equivalent measures may be used to write a ratio with a value of 1. This ratio can be used as a conversion factor.
60 min
1 hour
= 1
360 min 
= 6 hour
1 L
1000 mL
= 1
430 mL 
= L

17. 2.2 – Data Analysis Dimensional Analysis Converting Units
The same unit will always be written diagonally in the expression so that the unit cancels out in the calculation.
Write as many conversion factors as necessary to get to answer
Example: Convert seconds into days
Multiply across the top, then divide all the way across the bottom
Round the answer appropriately
360 min 
60 min
1 hour
= 6 hour
360 min 
1 hour
60 min
= min2/hr
seconds
minutes
hours
days
60 sec
1 min
60 min
1 hour
24 hour
1 day
sec   
= days
= 27 days

18. 2.2 – Data Analysis Dimensional Analysis The Box Method
Method of converting units similar to dimensional analysis using a series of boxes.
Place the measurement you are converting from in the top left corner of your boxes.
In the next set of boxes, place a ratio that relates your unit to the unit you want to convert to, so that the unit you are converting from cancels out.
Example: Convert seconds into days
Multiply across the top, then divide all the way across the bottom
Round the answer appropriately
sec
60 sec
1 min
60 min
1 hour
24 hour
1 day
= days
= 27 days

19. 2.3 – Reliability of Measurements
Objectives:
Differentiate between accuracy & precision
Calculate percent errors for data
Identify and use significant digits in calculations

20. 2.3 – Reliability of Measurements
Accuracy & Precision
Accuracy = comparison of a measure against a known standard
If you get the number that is expected when compared to a known standard, the measure is accurate (we calibrate scales to make sure they are accurate)
Precision = ability to reproduce the measurement
If you can reproduce over and over, the measure is said to be precise
If a measure is precise and accurate, then it is said to be reliable.

21. measured value – accepted value
2.3 – Reliability of Measurements
Calculating Percent Error
Comparison of a measurement to its accepted value.
Percent error is calculated using the formula:
Example: A cookie recipe anticipates a yield of 60 cookies. When the baking is finished only 54 cookies have been produced. Calculate the percent error.
measured value = 54 cookies
accepted value = 60 cookies
* While some people suggest taking the absolute value of this calculation, I prefer using the sign of the calculation.
Percent Error =
measured value – accepted value
x 100
accepted value
Percent Error =
54 cookies – 60 cookies
x 100 = -10%*
60 cookies

22. 2.3 – Reliability of Measurements
Certainty
Measurements always include a number of digits that are “certain” and a final digit that is “uncertain”.
The final digit is uncertain because:
some measuring instruments require estimation
some measuring instruments automatically round
Require Estimation
Automatically Round

23. 2.3 – Reliability of Measurements
Making Valid Measurements
When using a scaled instrument (ruler, meter stick, graduated cylinder, pipet, buret, etc.) always estimate one place beyond the certainty of the instrument.
The human eye is very capable of estimating tenths on most scaled instruments used in the lab. So ALWAYS estimate to the nearest 1/10 of the smallest graduation.
25.45 cm

24. 2.3 – Reliability of Measurements
Significant Digits
The certain digit(s) plus the final uncertain digit of a measurement are considered “significant”.
Rules for identifying sig figs.
Non-zero digits are always significant.
Zeros between non-zero digits are always significant.
Left hand zeroes are never significant.
Right hand zeroes are significant when a decimal is present.
Counts and defined constants have an infinite number of significant digits. Don’t use them for rounding.
3010 g g g g
7.123 g
3010 g g g g g
0.301 g g g g g
300.0 g
190 g g g g

25. 2.3 – Reliability of Measurements
Rounding Answers
At the end of calculations, the answer must be rounded to the correct number of significant digits.
Deciding where to round.
In addition and subtraction, round the answer to match the measurement with the fewest decimal places.
In multiplication and division, round the answer to match the measurement with the fewest significant digits.
3010 g g
= g
3040 g g g
= g g
1.01 g g
= g
0.98 g
13 g
- 6 g
= 7 g
7 g
3.6 cm
x 30.6 cm
= cm2
110 cm2
2.51 cm
x 0.6 cm
= cm2
2 cm2
1.01 cm3
 cm
= cm2
33.0 cm2
13 cm3
 6 cm
= cm2
2 cm2

26. 2.3 – Reliability of Measurements
Rounding Answers
Deciding how to round.
After finding the correct rounding position, look at the digits that follow it.
If the digits are less than 5, do not change the final digit.
If the digits are greater than 5, round the final digit up.
If the digits exactly equal 5, round the final digit to be even.
g  313 g
g  0.01 g
g  314 g
g  0.02 g
g  314 g
g  0.04 g

27. 2.4 – Representing Data Objectives:
Select appropriate graph types for representing data
Determine how different trends appear on graphs
Understand why we use best fit lines
Calculate slopes for data lines

28. 2.4 – Representing Data Graphing Pie charts
Used to represent categorical data as parts of a whole. Pie charts typically depict percentages (fractions). A pie chart is constructed by converting the share of each component part into a percentage of 360o.

29. 2.4 – Representing Data Graphing Bar Graphs
Used to represent categorical or numeric values within certain intervals. Bars may be drawn horizontally or vertically. Each bar represents a category, value or range of values. They are often used to show changes over time and clearly illustrate differences in magnitude.

30. 2.4 – Representing Data Graphing Line Graphs
Most common graph used in science. They show the relationship between two variables. Line graphs are useful for showing trends.
Relationships are typically shown using best-fit lines which may not intersect any of the data points.

31. 2.4 – Representing Data Graphing Trends
Reliable data will generally show one of a limited number of trends or relationships:
Direct Relationships (Positive Correlation)

32. 2.4 – Representing Data Graphing Trends
Inverse Relationships (Negative Correlation)

33. 2.4 – Representing Data Graphing Trends Exponential Relationships
Decay
Growth

34. 2.4 – Representing Data Best Fit Lines & Slope
Best fit lines are used to show the underlying trend of the data in a scatterplot. The trend can then be used to make predictions.
Drawing a best fit line simply requires drawing a line through the center of the plotted data so that data points are evenly distributed above and below the line.
Making predictions beyond the data points is called extrapolation.
Making predictions between the data points is called interpolation.

35. where ∆ means “change in”.
2.4 – Representing Data
Slope
The slope of the line may be calculated using the formula
slope = ∆y / ∆x
where ∆ means “change in”.