Measurement and Chemical Calculations

1
CHAPTER 1

• Measurement and Chemical Calculations

2
What is Chemistry

• Chemistry is the study of matter and its changes

3
What is Matter?

• Matter is anything that occupies space and has
  weight.

4
Examples of Matter

• Pens and pencils
• Paper
• Students
• Desks
• Cars
• Airplanes

5
Is Air Matter?

• Air would be matter if it takes up space and has
  weight.

6
Is Air Matter?

• Air would be matter if it takes up space and has
  weight.
• Does it?

7
Is Air Matter?

• Air would be matter if it takes up space and has
  weight.
• Does it?
• The space that air takes up is called the
  atmosphere.
• Does air have weight?

8
Is Air Matter?

• Air would be matter if it takes up space and has
  weight.
• Does it?
• The space that air takes up is called the
  atmosphere.
• Does air have weight?
• Yes air does have weight, if not, then it would
  flow into outer space.

9
Is Air Matter?

• Air would be matter if it takes up space and has
  weight.
• Does it?
• The space that air takes up is called the
  atmosphere.
• Does air have weight?
• Yes air does have weight, if not, then it would
  flow into outer space. One liter of air weighs
  1.29 grams.

10
What are Changes?

• In the study of chemistry we talk about two
  different kinds of changes, physical and chemical

11
What are Changes?

• In the study of chemistry we talk about two
  different kinds of changes, physical and chemical
• Physical change is a change to matter so that the
  identity is not altered i.e. taste, smell.

12
What are Changes?

• In the study of chemistry we talk about two
  different kinds of changes, physical and chemical
• Physical change is a change to matter so that the
  identity is not altered i.e. taste, smell.
• Chemical change is a change to matter so that its
  identity is changed i.e. different smell, color,
  taste.

13
Examples of Physical Change

• Tearing paper starts out paper and ends as paper
• Folding paper starts out paper and ends as
  paper
• Melting of ice starts out water and ends as
  water
• Evaporation of water starts out water and ends
  as water

14
Examples of Chemical Change

• Wood burning starts out as wood ends up as smoke
  and ashes, different smell and taste, right?
• Steel rusting starts out as steel ends up as
  rust, different smell and taste
• Healing of a wound starts out a blood ends up as
  scar tissue, different color, taste and smell

15
Matter Continued

• Is everything matter?

16
Matter Continued

• Is everything matter? No, not everything we can
  think of has weight and takes up space.

17
Matter Continued

• Is everything matter? No, not everything we can
  think of has weight and takes up space.
• For example personality!

18
Matter Continued

• Is everything matter? No, not everything we can
  think of has weight and takes up space.
• For example personality! One might argue that
  personality takes up the space of ones brain or
  person, but

19
Matter Continued

• Is everything matter? No, not everything we can
  think of has weight and takes up space.
• For example personality! One might argue that
  personality takes up the space of ones brain or
  person, butnot all personable people are
  overweight. Thus personality does not have
  weight, and is therefore not matter.

20
Matter Continued

• How about thought? Again we might argue that
  thought takes up the space of ones brain and your
  mother told you about heavy thoughts, but.

21
Matter Continued

• How about thought? Again we might argue that
  thought takes up the space of ones brain and your
  mother told you about heavy thoughts, but.If you
  get on the bathroom scale and start having heavy
  thoughts, your weight does not go up!

22
Matter Continued

• How about thought? Again we might argue that
  thought takes up the space of ones brain and your
  mother told you about heavy thoughts, but.If you
  get on the bathroom scale and start having heavy
  thoughts, your weight does not go up! That means
  thought is not matter, so if someone studies
  thought, they are not doing chemistry.

23
Examples of Chemistry

• The study of why wood burns
• The study of why cement does not burn
• The study of why nails rust
• The study of milk spoiling
• These all fit the definition of chemistry since
  they deal with change and matter

24
History of Chemistry

• Who were the first chemists?

25
History of Chemistry

• Who were the first chemists?

26
History of Chemistry

• Who were the first chemists?

Cavemen
27
History of Chemistry

• What kind of matter and changes did the cavemen
  study?

28
History of Chemistry

• What kind of matter and changes did the cavemen
  study? Fire and food!
• Archeologists have found evidence of fire in
  caves and animal bones too. Cooking meat makes
  meat chewable. Chewing raw meet wears out ones
  jaw.

29
History of Chemistry

• The next group that left archeological evidence
  of chemistry were the Egyptians. Their chemistry
  involved mummies, textile dyes, ink, paper and
  paints most of which can be found inside the
  pyramids.

30
History of Chemistry

• The first group of people to leave written
  records of their chemistry were the Greeks. From
  Greek writings, we can see that the Greeks made
  observations, and created reasons for these
  observations, called hypothesis. They did not
  attempt to prove their hypothesis by
  experimentation, thus their chemistry efforts
  were philosophical in nature as opposed to
  science in nature.

31
History of Chemistry

• The first group of chemists to test hypothesis
  with experiments were the alchemists. Alchemists
  were a group of Europeans that were trying to
  change matter in to different kinds of matter.
  For example, they were trying to change lead into
  gold. The major results of their experiments
  were to prove most of the Greek ideas of
  chemistry to be false and to show a clear
  distinction between science and philosophy.

32
History of Chemistry

• A major short coming of the Alchemists chemistry
  was irreproducible results, caused by lack of
  measurement understanding. For example, on day 1
  mixing two kinds of matter produced black
  matter, while doing the same thing the next day
  produced red matter. The Alchemists were the
  first group of chemists to make observations,
  create hypothesis, and to test their hypothesis
  with experiments.

33
Modern Chemistry

• Antoine Lavoisier was the founder of modern
  chemistry by making careful measurements.

34
Modern Chemistry

• Lavoisiers careful measurements now made
  experiments reproducible. Chemists in other
  countries could now do the same experiment and
  get the same results. This now allowed chemists
  to prove a hypothesis to be correct by
  experimentation, thus leading to the discovery of
  theories and laws.

35
Modern Chemistry
Lavoisiers Theories and Laws

• Law of Conservation of Mass
• Atomic Theory

36
Scientific Method

• Is a sequence of thoughts and experiments
  containing the following
• A hypothesis is a tentative and testable
  explanation for an observation or a series of
  observations.
• A scientific theory is a general explanation of
  widely observed phenomena that have been
  extensively tested.

37
Classification of Matter
Matter
Heterogeneous
Homogeneous
Solutions
Substances
Elements
Compounds
38
Classification of Matter
Homogeneous and Heterogeneous

• Homogeneous matter looks the same everywhere with
  a microscope, but since we lack microscopes we
  will use our eyes and not our imagination.
  Heterogeneous matter does not look the same
  everywhere.

39
Classification of Matter
Homogeneous or Heterogeneous?
Wood
Margarine
Carpet
Gold
40
Classification of Matter
Homogeneous or Heterogeneous?
Wood
Margarine
Carpet
Gold
Heterogeneous
41
Classification of Matter
Homogeneous or Heterogeneous?
Wood
Margarine
Carpet
Gold
Heterogeneous
Heterogeneous
42
Classification of Matter
Homogeneous or Heterogeneous?
Wood
Carpet
Margarine
Gold
Heterogeneous
Heterogeneous
Homogeneous
43
Classification of Matter
Homogeneous or Heterogeneous?
Wood
Carpet
Margarine
Gold
Heterogeneous
Heterogeneous
Homogeneous
Homogeneous
44
Classification of Matter

• Solution is a homogeneous random combination of
  two or more different types of matter.
• For example a random amount of salt and water
  combined together produces a homogeneous mixture,
  called salt water. Random combination means some
  salt and some water.

45
Classification of Matter

• Any combination the produces a homogeneous result
  that is not randomly created is called a
  substance.
• For example, combining two hydrogen atoms and one
  oxygen atom produces a compound of water, which
  is a substance. Or the combination of two oxygen
  atoms, gives a molecule of oxygen.

46
Classification of Matter

• Homogeneous matter created by the same atom is
  called and element. Exact combinations of
  different elements is called a compound.

47
Classification of Matter

• Label the following examples of matter as
  heterogeneous, solution, compound or element.
• Sand
• Sea water
• Tap water
• Steel
• Antimony
• Air
• Distilled water
• Cement
• Wine

48
Classification of Matter

• Label the following examples of matter as
  heterogeneous, solution, compound or element.
• Sand-Heterogeneous
• Sea water
• Tap water
• Steel
• Antimony
• Air
• Distilled water
• Cement
• Wine

49
Classification of Matter

• Label the following examples of matter as
  heterogeneous, solution, compound or element.
• Sand-Heterogeneous
• Sea water-Heterogeneous
• Tap water
• Steel
• Antimony
• Air
• Distilled water
• Cement
• Wine

50
Classification of Matter

• Label the following examples of matter as
  heterogeneous, solution, compound or element.
• Sand-Heterogeneous
• Sea water-Heterogeneous
• Tap water-Solution
• Steel
• Antimony
• Air
• Distilled water
• Cement
• Wine

51
Classification of Matter

• Label the following examples of matter as
  heterogeneous, solution, compound or element.
• Sand-Heterogeneous
• Sea water-Heterogeneous
• Tap water-Solution
• Steel-Solution
• Antimony
• Air
• Distilled water
• Cement
• Wine

52
Classification of Matter

• Label the following examples of matter as
  heterogeneous, solution, compound or element.
• Sand-Heterogeneous
• Sea water-Heterogeneous
• Tap water-Solution
• Steel-Solution
• Antimony-Element
• Air
• Distilled water
• Cement
• Wine

53
Classification of Matter

• Label the following examples of matter as
  heterogeneous, solution, compound or element.
• Sand-Heterogeneous
• Sea water-Heterogeneous
• Tap water-Solution
• Steel-Solution
• Antimony-Element
• Air-Solution
• Distilled water
• Cement
• Wine

54
Classification of Matter

• Label the following examples of matter as
  heterogeneous, solution, compound or element.
• Sand-Heterogeneous
• Sea water-Heterogeneous
• Tap water-Solution
• Steel-Solution
• Antimony-Element
• Air-Solution
• Distilled water-Compound
• Cement
• Wine

55
Classification of Matter

• Label the following examples of matter as
  heterogeneous, solution, compound or element.
• Sand-Heterogeneous
• Sea water-Heterogeneous
• Tap water-Solution
• Steel-Solution
• Antimony-Element
• Air-Solution
• Distilled water-Compound
• Cement-Heterogeneous
• Wine

56
Classification of Matter

• Label the following examples of matter as
  heterogeneous, solution, compound or element.
• Sand-Heterogeneous
• Sea water-Heterogeneous
• Tap water-Solution
• Steel-Solution
• Antimony-Element
• Air-Solution
• Distilled water-Compound
• Cement-Heterogeneous
• Wine-Solution

57
Classification of Matter

• Types of Matter
• Pure Substances have the same physical and
  chemical properties throughout.
• Mixtures are composed of two or more substances
  (elements or compounds) in variable proportions.

58
Elements and Compounds

• Most elements are not found in the world in the
  pure form. They are found in compounds.
• Hydrogen is found in water, H2O, and other
  hydrogen containing compounds.
• The law of constant composition states that every
  sample of a compound always contains the same
  elements in the same proportions.

59
Pure Substances

• Two Groups
• An element is the simplest kind of material with
  unique physical and chemical properties.
• A compound is a substance that consists of two or
  more elements linked together in definite
  proportions.

60
An Atomic View

• An atom is the smallest particle of an element
  that retains the chemical characteristics of that
  element.
• A molecule is a collection of atoms chemically
  bonded together having constant proportions.

61
Properties of Matter

• Intensive property - a characteristic that is
  independent of the amount of substance present.
• Examples color, hardness, etc.
• Extensive property - a characteristic that varies
  with the quantity of the substance present.
• Examples length, width, mass, etc.

62
State of Matter

• Solids have definite shapes and volumes.
• Liquids occupy definite volumes, but do not have
  definite shapes.
• Gases have neither a definite shape nor volume.
• Plasma, not found on earth, but stars, similar to
  a gas, but a mixture of subatomic particles

63
Examples
64
Making Measurements

• Accurate measurements are essential for our
  ability to characterize the physical and chemical
  properties of matter.
• Standardization of the units of measurements is
  essential.

65
About Measurements
All measurements contain two parts a number and a
unit. The number comes from a measuring device,
such as a ruler, clock, or speedometer, to name a
few examples of measuring devices. The unit is a
word or abbreviated word describing the kind of
measurement. All measuring devices contain a
scale. Scales contain space between the lines.
The last number of a measurement, called a
significant figure, is a guess as to the number
between the lines.
66
About the Measurement Number
What is the measurement of the object below?
Object
67
About the Measurement Number
What is the measurement of the object below?
11.64 cm
Object
The last figure of the measurement number is a
guess and therefore measurements cannot be exact.
68
About the Measurement Number
Object
11.64 cm
Since the last number is a guess most
observerswould agree between 11.63-11.65 cm.
This being the case 11.64 is usually expressed as
11.640.01 cm
69
About the Measurement Number
When we make a scientific measurement the last
recorded number is always an estimate.
This means that the last recorded number will
usually vary depending on who is estimating the
last number. This produces uncertainty, or error
in the measurement.
70
About the Measurement Number

• The closer together the lines are on the
  measuring scale the more
• numbers that are required to describe the
  measurement, but the last
• number is still always a guess. We refer to the
  number of numbers in
• a measurement as the number of significant
  figures. The more
• significant figures the higher quality of the
  measurement.
• One of the confusing issues about numbers is
  zero, since it can be a
• number, decimal position holder or both. If zero
  is to be considered both
• a position holder and a number additional
  information about the
• measurement mush be known.

71
About Significant Figures
Since zero is used as a decimal place holder, a
number, or both. How do we determine if a zero
is a number or a position holder when determining
the number of significant figures for a
measurement?

Consider dropping one or more of the zero digits.
If dropping a zero changes the value of the
measurement, then the zero is a decimal position
holder and is not considered to be a number and
therefore cannot be counted as a number in the
significant figure count.
Consider the measurement of 100 cm. If one of
the zeros is dropped then the measurement becomes
10 cm, which has a different value than the
original 100 cm. If both zeros are dropped then
the measurement becomes 1 cm which is not the
same as the original 100cm, therefore only one
number and one significant figure.
72
About Significant Figures
Now consider the measurement 100.0 cm. If the
last zero is dropped the value of the measurement
remains the same. Here the last zero does not
space the decimal in this measurement. Since
zeros are either decimal position holders, or
numbers, then the zero in this case must be a
number and counted in the significant figure
count since is not a decimal spacer.
What about the zeros in the center of the
measurement of 100.0 cm? Since the last zero is
a number and the one at the beginning is a number
then the center zeros are sandwiched by two
numbers. Sandwiched zeros are always counted as
significant figures, thus giving 100.0 cm four
significant figures.
73
Significant Figure Pratice Sometimes zeros can be
both spacers and numbers. To differentiate
between spacers and zeros, additional information
must be given.
Consider the following list of measurements and
determine how many significant figures each
measurement contains.
Measurements
SigFigs
10 cm 10.0 cm 101 cm 101.0 cm 1.00 X 10-3 cm
74
Examples Sometimes zeros can be both spacers and
numbers. To differentiate between spacers and
zeros, additional information must be given.
Consider the following list of measurements and
determine how many significant figures each
measurement contains.
Measurements
SigFigs
Reason
1
10 cm 10.0 cm 101 cm 101.0 cm 1.00 X 10-3 cm
Zero is a spacer for sure. Additional
information required to see if it is a number

75
Examples Sometimes zeros can be both spacers and
numbers. To differentiate between spacers and
zeros, additional information must be given.
Consider the following list of measurements and
determine how many significant figures each
measurement contains.
Measurements
SigFigs
Reason
1
10 cm 10.0 cm 101 cm 101.0 cm 1.00 X 10-3 cm
Zero is a spacer for sure. Additional
information required to see if it is a number
3
The last number is not a spacer, since dropping
it the value is unchanged. The other zero is
sandwiched.
76
Examples Sometimes zeros can be both spacers and
numbers. To differentiate between spacers and
zeros, additional information must be given.
Consider the following list of measurements and
determine how many significant figures each
measurement contains.
Measurements
SigFigs
Reason
1
10 cm 10.0 cm 101 cm 101.0 cm 1.00 X 10-3 cm
Zero is a spacer for sure. Additional
information required to see if it is a number
3
3
Zero is sandwiched here
77
Examples Sometimes zeros can be both spacers and
numbers. To differentiate between spacers and
zeros, additional information must be given.
Consider the following list of measurements and
determine how many significant figures each
measurement contains.
Measurements
SigFigs
Reason
1
10 cm 10.0 cm 101 cm 101.0 cm 1.00 X 10-3 cm
Zero is a spacer for sure. Additional
information required to see if it is a number
3
3
Zero is sandwiched here
4
Zero is a spacer for sure. Additional
information required to see if it is a number.
78
Examples Sometimes zeros can be both spacers and
numbers. To differentiate between spacers and
zeros, additional information must be given.
Consider the following list of measurements and
determine how many significant figures each
measurement contains.
Measurements
SigFigs
Reason
1
10 cm 10.0 cm 101 cm 101.0 cm 1.00 X 10-3
cm 0.0010
Zero is a spacer for sure. Additional
information required to see if it is a number
3
3
Zero is sandwiched here
4
Zero is a spacer for sure. Additional
information required to see if it is a number.
3
Only look at the coefficient
2 The last zero is counted
79
MEASUREMNTS QUALITY

• Accuracy-How close a measurement is to the true
  value.
• Precision-How close multiple measurements of the
  same object are to each other. Or the number of
  significant figures.

80
Accuracy and Precision
81
Now About the Unit
In chemistry we use the international system of
units. This is a modern version of the metric
system. Unfortunately this system of units is
not widely used in everyday life in the USA.
Being able to use conversion factors and
formulas to transform measurements between
systems of units is extremely important. This
procedure is called unit analysis, most commonly
referred to as conversions
82
About the Metric Units
Some of the common units for measurements and
their abbreviations are shown below.
Measurement Units Abbreviation
Mass grams g
Volume liters L
Distance meters m
Time seconds s
A much more extensive table is given on page 17
of the text.
83
Memorized Metric Prefixes
In chemistry we are often dealing with very large
or very small quantities. To help with this a
system of prefix modifiers has been developed to
make measurements user friendly.
Prefix Abbreviation Coefficient
mega M 1000 000 (106)
kilo k 1000 (103)
deci d 0.1 (10-1)
centi c 0.01 (10-2)
milli m 0.001 (10-3)
micro µ 0.000001 (10-6)
84
Application of Metric Prefixes
Length (m) Mass (g) Time (s)
103 m km 103 g kg 103 s ks 10-2 m
cm 10-2 g cg 10-2 s cs 10-3 m mm 10-3 g
mg 10-3 s ms 10-6 m µm 10-6 g µg 10-6 s µs
Note The memorized number always is in front of
the single letter.
85
Unit Conversions
There have been many serious incidents that have
resulted from errors in converting between
systems of units.
Air Canada Flight 143 (Google it for more details)
Due to accidents, careful unit conversions are
important.
86
Unit Conversions
125 million Mars Climate Orbiter. Lost in Space.
Yet another example of improper unit conversions
Do you think there is the potential to make
errors in the conversion of units for health care
providers?
87
Conversion Problem Steps

• Write down the number and unit.
• Draw lines a vertical line after the number an
  unit and horizontal line below the number and
  unit.
• Insert a fractional fact to cancel out the
  original unit.
• Compare the new unit to the asked for unit
• a. If the same, you are done.
• b. If not the same, repeat step 3.

88
Step 1. Write down the number and unit.
47.2 mg
89
Step 1. Write down the number and unit.
47.2 mg
Step 2. Draw lines
47.2 mg
90
Step 1. Write down the number and unit.
47.2 mg
Step 2. Draw lines
47.2 mg
Step 3. Insert fractional fact crossing out
original unit
91
Step 1. Write down the number and unit.
47.2 mg
Step 2. Draw lines
47.2 mg
Step 3. Insert fractional fact crossing out
original unit
47.2 mg
10-3 g
mg
92
Step 1. Write down the number and unit.
47.2 mg
Step 2. Draw lines
47.2 mg
Step 3. Insert fractional fact crossing out
original unit
47.2 mg
10-3 g
mg
Step 4. Compare new unit to the asked for unit.
93
Step 1. Write down the number and unit.
47.2 mg
Step 2. Draw lines
47.2 mg
Step 3. Insert fractional fact crossing out
original unit
47.2 mg
10-3 g
mg
Step 4. Compare new unit to the asked for
unit. A. If the same you are done b. If not
the same repeat step 3.
94
Step 1. Write down the number and unit.
47.2 mg
Step 2. Draw lines
47.2 mg
Step 3. Insert fractional fact crossing out
original unit
47.2 mg
10-3 g
0.0472 g
mg
Step 4. Compare new unit to the asked for
unit. A. If the same you are done b. If not
the same repeat step 3.
95
Step 1. Write down the number and unit.
702 cL
Step 2. Draw lines
702 cL
Step 3. Insert fractional fact crossing out
original unit
702 cL
10-2 L
cL
Step 4. Compare new unit to the asked for
unit. A. If the same you are done b. If not
the same repeat step 3.
96
Not a match repeat step 3
Step 1. Write down the number and unit.
702 cL
Step 2. Draw lines
702 cL
Step 3. Insert fractional fact crossing out
original unit
702 cL
10-2 L
cL
Step 4. Compare new unit to the asked for
unit. A. If the same you are done b. If not
the same repeat step 3.
97
Its a match, done
Step 1. Write down the number and unit.
702 cL
Step 2. Draw lines
702 cL
Step 3. Insert fractional fact crossing out
original unit
µL
702 cL
10-2 L
cL
10-6 L
Step 4. Compare new unit to the asked for
unit. A. If the same you are done b. If not
the same repeat step 3.
98
Its a match, done
Step 1. Write down the number and unit.
702 cL
Step 2. Draw lines
702 cL
Step 3. Insert fractional fact crossing out
original unit
µL
702 cL
10-2 L
7.02 x 106 µL
cL
10-6 L
Step 4. Compare new unit to the asked for
unit. A. If the same you are done b. If not
the same repeat step 3.
99
English/Metric Conversions

• When converting between English and the metric
• systems the following definitions should be used.
• 2.54 cm in
• 946 mL qt
• 454 g lb
• Example Convert 155 lbs to kg.

155 lbs
100
English/Metric Conversions

• When converting between English and the metric
• systems the following definitions should be used.
• 2.54 cm in
• 946 mL qt
• 454 g lb
• Example Convert 155 lbs to kg.

155 lbs
454 g
lb
101
English/Metric Conversions

• When converting between English and the metric
• systems the following definitions should be used.
• 2.54 cm in
• 946 mL qt
• 454 g lb
• Example Convert 155 lbs to kg.

155 lbs
454 g
kg
lb
103 g
102
English/Metric Conversions

• When converting between English and the metric
• systems the following definitions should be used.
• 2.54 cm in
• 946 mL qt
• 454 g lb
• Example Convert 155 lbs to kg.

155 lbs
454 g
kg
70.37 kg
lb
103 g
103
English/Metric Conversions

• When converting between English and the metric
• systems the following definitions should be used.
• 2.54 cm in
• 946 mL qt
• 454 g lb
• Example Convert 155 lbs to kg.

155 lbs
454 g
kg
70.37 kg
70.4 kg
lb
103 g
104
Sample English/Metric Conversion Problems

1. Convert 708 pounds to kilograms.
2. Convert 50.0 liters to gallons.
3. Convert the density of water to pounds per
   gallon.
4. How many cubic meters are contained in 33 liters?
5. The density of aluminum is 2.70 g/mL. Find the
   thickness of aluminum foil that measures 2.0 cm
   by 5.66 cm.

105
ROUNDING
When measurements are combined to provide
information, can the calculated result be of a
higher quality than the measurements?
106
ROUNDING
When measurements are combined to provide
information, can the information be of a higher
quality than the measurements? No, information
provide by combining measurements cannot have an
accuracy, or precision greater than the
measurement that provided the information.
107
Why Round After a Calculation
Since information provided by combining
measurements cannot have a higher quality than
the measurements providing the information, then
answers to problems must be rounded to give the
same quality as the measurement with the least
quality.
Rounding rules are designed to give answers the
desired quality. They are posted on the course
website and restated on the following slides.
108
ROUNDING RULES
Rounding is the process of providing results that
have the same quality as measurements with the
least quality. Since there are different
mathematical methods of combining measurements,
then different rounding rules are required to
provide sensible results of measurement
combinations.
109
Addition and Subtraction
Round the calculated answer so that it contains
the same number of decimal places as the
measurement with the least number of decimal
places.
110
Addition and Subtraction
Round the calculated answer so that it contains
the same number of decimal places as the
measurement with the least number of decimal
places.
22.33 cm 124 cm
111
Addition and Subtraction
Round the calculated answer so that it contains
the same number of decimal places as the
measurement with the least number of decimal
places.
22.33 cm 124 cm 146 cm
112
Multiplication and Division

• Round the calculated answer so that it contains
  the same number of significant figures as the
  measurement with the least number of significant
  figures. In other words, if the measurement with
  the least number of significant figures contains
  two significant figures, then the rounded answer
  should contain two significant figures.
• 22.33 cm
• x 124 cm

113
Multiplication and Division

• Round the calculated answer so that it contains
  the same number of significant figures as the
  measurement with the least number of significant
  figures. In other words, if the measurement with
  the least number of significant figures contains
  two significant figures, then the rounded answer
  should contain two significant figures.
• 22.33 cm
• x 124 cm
• 2770 cm

114
Logarithms

• Round the calculated answer so that it contains
  the same
• number of decimal places as the measurement with
  the least
• number of significant figures. In other words,
  if the
• measurement with the least number of significant
  figures
• contains two significant figures, then the
  rounded answer
• should contain two decimal places.

115
Anti-logarithms

• Round answer so that the number of significant
  figures
• matches the number of decimal places as the
  measurement
• with the least number of decimal places. In
  other words, if the
• measured number contains three decimal places,
  then the
• answer should be rounded so that it contains
  three significant
• figures.

116
Scientific Notation
117
Scientific Notation Examples

• Convert the following into scientific notation.
• 454,000 mi

118
Scientific Notation Examples

• Convert the following into scientific notation.
• 454,000 mi

4.54
Step 1, place a decimal to the right of the first
non-zero number.
119
Scientific Notation Examples

• Convert the following into scientific notation.
• 454,000 mi

4.54 X 10
Step 1, place a decimal to the right of the first
non-zero number. Step 2, place X 10 after the
number.
120
Scientific Notation Examples

• Convert the following into scientific notation.
• 454,000 mi

4.54 X 105
Step 1, place a decimal to the right of the first
non-zero number. Step 2, place X 10 after the
number. Step 3, count from the old decimal
location to the new decimal location, this number
of places becomes the power of 10.
121
Scientific Notation Examples

• Convert the following into scientific notation.
• 454,000 mi

4.54 X 105 mi
Step 1, place a decimal to the right of the first
non-zero number. Step 2, place X 10 after the
number. Step 3, count from the old decimal
location to the new decimal location, this number
of places becomes the power of 10.
Note Be sure that the answer contains the same
number of significant figures as the starting
measurement
122
Scientific Notation Examples
Convert the following into scientific
notation. b. 0.00283 mi
Step 1, place a decimal to the right of the first
non-zero number.
123
Scientific Notation Examples
Convert the following into scientific
notation. b. 0.00283 mi
Step 1, place a decimal to the right of the first
non-zero number.

2.83 mi
124
Scientific Notation Examples
Convert the following into scientific
notation. b. 0.00283 mi
Step 1, place a decimal to the right of the first
non-zero number. Step 2, place X 10 after the
number.

2.83 X 10 mi
125
Scientific Notation Examples
Convert the following into scientific
notation. b. 0.00283 mi
Step 1, place a decimal to the right of the first
non-zero number. Step 2, place X 10 after the
number. Step 3, count from the old decimal
location to the new decimal location, this number
of places becomes the power of 10, unless the
number is less than one, if so, then negative
power
Note Be sure that the answer contains the same
number of significant figures as the starting
measurement
2.83 X 10-3 mi
126
DENSITY

• What is heavier 5 pounds of lead or 5 pounds of
  feathers?
• What takes up more space, 5 pounds of lead or 5
  pounds of feathers?

127
DENSITY

• What is heavier 5 pounds of lead or 5 pounds of
  feathers? Both the same. This is an old riddle
  to confuse density with weight
• What takes up more space, 5 pounds of lead or 5
  pounds of feathers?

128
DENSITY

• What is heavier 5 pounds of lead or 5 pounds of
  feathers? Both the same. This is an old riddle
  to confuse density with weight
• What takes up more space, 5 pounds of lead or 5
  pounds of feathers? Feathers, since they are less
  dense.

129
DENSITY UNITS

• g/ml, g/cm3, (for solids and liquids), or
• g/L for gases

130
Volume Determination
We can determine the volume of irregularly shaped
objects by displacement.
How can we determine the volume of a gas?
Gases fill whatever container they are placed in.
So its the volume of the container !
131
DENSITY PROBLEM SOLVING STRATEGY
Use the four step unit analysis method from
yesterday. Organize the measurements to give
density units.
Sample Problems

• Calculate the density of a 4.07 g sample of rock
  that displaces 1.22 mL of water.
• Calculate the density of a 4.22 g sample of wood
  that measures 2.0 cm by 1.33 cm by 3.56 cm.
• Mercury has a density of 13.6 g/mL. Find the
  mass of 125 mL of mercury.
• Water has a density of 1.00 g/mL. Find the
  volume, in liters, of a 3.22 kg sample of water.
• What does an object do in water with
• A density greater than water?
• A density less than water?
• A density equal to water?

132
PERCENT CALCULATIONS
Percent is an simplified form of a fraction,
which can be used in the unit analysis process
(four step method) as a fractional fact
Percent has a mathematical form of
part
X 100
?
total
For example, if there are 37 red marbles and 68
green marbles, then the total number of marbles
is 105 marbles. The percent of red marbles would
be
?
37
?
X 100

35
105
133
Percent as a Fraction
Also, percent can be used as a fractional fact.
For example if there are 35 red marbles, then
how many red marbles would be in a collection of
687 total marbles?
687 total
35 red
240.45 marbles

100 total
Rounding?
134
Percent as a Fraction
Also, percent can be used as a fractional fact.
For example if there are 35 red marbles, then
how many red marbles would be in a collection of
687 total marbles?
687 total
35 red
240.45 marbles

100 total
Rounding? First of all marbles are counted and
Have no significant figures. Since we do not
have Fractional marbles, then this needs to be
rounded to the nearest marble
135
Percent as a Fraction
Also, percent can be used as a fractional fact.
For example if there are 35 red marbles, then
how many red marbles would be in a collection of
687 total marbles?
687 total
35 red
240 marbles

100 total
Rounding? First of all marbles are counted and
Have no significant figures. Since we do not
have Fractional marbles, then this needs to be
rounded to the nearest marble
136
The End