CHAPTER #1
Measurement and Chemical Calculations
What is Chemistry
Chemistry is the study of matter and its changes
What is Matter?
Matter is anything that occupies space and has
weight.
Examples of Matter
•
•
•
•
•
•
Pens and pencils
Paper
Students
Desks
Cars
Airplanes
Is Air Matter?
Air would be matter if it takes up space and
has weight.
Is Air Matter?
Air would be matter if it takes up space and
has weight.
Does it?
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?
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.
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.
What are Changes?
In the study of chemistry we talk about two
different kinds of changes, physical and chemical
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….
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.
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
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
Matter Continued
Is everything matter?
Matter Continued
Is everything matter? No, not everything we
can think of has weight and takes up space.
Matter Continued
Is everything matter? No, not everything we
can think of has weight and takes up space.
For example personality!
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…
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…not all personable people are
overweight. Thus personality does not have
weight, and is therefore not matter.
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….
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!
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.
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
History of Chemistry
Who were the first chemists?
History of Chemistry
Who were the first chemists?
History of Chemistry
Who were the first chemists?
Cavemen
History of Chemistry
What kind of matter and changes did the
cavemen study?
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.
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.
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.
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.
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.
Modern Chemistry
Antoine Lavoisier was the founder of modern
chemistry by making careful measurements.
Modern Chemistry
Lavoisier’s 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.
Modern Chemistry
Lavoisier’s Theories and Laws
• Law of Conservation of Mass
• Atomic Theory
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.
Classification of Matter
Matter
Homogeneous
Substances
Elements
Heterogeneous
Solutions
Compounds
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.
Classification of Matter
Homogeneous or Heterogeneous?
Wood
Carpet
Margarine
Gold
Classification of Matter
Homogeneous or Heterogeneous?
Wood
Heterogeneous
Carpet
Margarine
Gold
Classification of Matter
Homogeneous or Heterogeneous?
Wood
Carpet
Heterogeneous Heterogeneous
Margarine
Gold
Classification of Matter
Homogeneous or Heterogeneous?
Wood
Carpet
Heterogeneous Heterogeneous
Margarine
Homogeneous
Gold
Classification of Matter
Homogeneous or Heterogeneous?
Wood
Carpet
Heterogeneous Heterogeneous
Margarine
Gold
Homogeneous Homogeneous
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.
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.
Classification of Matter
Homogeneous matter created by the same atom
is called and element. Exact combinations of
different elements is called a compound.
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
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
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
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
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
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
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
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
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
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
Classification of Matter
•
Types of Matter
1. Pure Substances have the same physical and
chemical properties throughout.
2. Mixtures are composed of two or more
substances (elements or compounds) in
variable proportions.
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.
Pure Substances
Two Groups
1. An element is the simplest kind of material with
unique physical and chemical properties.
2. A compound is a substance that consists of two or
more elements linked together in definite proportions.
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.
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.
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
Examples
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.
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.
About the Measurement Number
What is the measurement of the object below?
Object
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.
About the Measurement Number
Object
11.64 cm
Since the last number is a guess most observers
would agree between 11.63-11.65 cm. This being the case 11.64
is usually expressed as 11.64±0.01 cm
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.
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.
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.
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.
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
10 cm
10.0 cm
101 cm
101.0 cm
1.00 X 10-3 cm
SigFigs
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
10 cm
10.0 cm
101 cm
101.0 cm
1.00 X 10-3 cm
SigFigs
1
Reason
Zero is a spacer for sure. Additional information
required to see if it is a number
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
10 cm
1
Zero is a spacer for sure. Additional information
required to see if it is a number
10.0 cm
3
The last number is not a spacer, since dropping
it the value is unchanged. The other zero is
sandwiched.
101 cm
101.0 cm
1.00 X 10-3 cm
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
10 cm
1
10.0 cm
3
101 cm
3
101.0 cm
1.00 X 10-3 cm
Reason
Zero is a spacer for sure. Additional information
required to see if it is a number
Zero is sandwiched here
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
10 cm
1
10.0 cm
3
101 cm
3
101.0 cm
4
1.00 X 10-3 cm
Reason
Zero is a spacer for sure. Additional information
required to see if it is a number
Zero is sandwiched here
Zero is a spacer for sure. Additional
information required to see if it is a number.
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
Zero is a spacer for sure. Additional information
required to see if it is a number
10 cm
1
10.0 cm
3
101 cm
3
101.0 cm
4
1.00 X 10-3 cm
3
Zero is a spacer for sure. Additional
information required to see if it is a number.
Only look at the coefficient
0.0010
2
The last zero is counted
Zero is sandwiched here
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.
Accuracy and Precision
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
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.
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
kilo
M
k
1000 000 (106)
1000 (103)
deci
d
0.1 (10-1)
centi
c
0.01 (10-2)
milli
micro
m
μ
0.001 (10-3)
0.000001 (10-6)
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 = mg10-3 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.
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.
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?
Conversion Problem Steps
1. Write down the number and unit.
2. Draw lines; a vertical line after the number an unit
and horizontal line below the number and unit.
3. Insert a fractional fact to cancel out the original unit.
4. Compare the new unit to the asked for unit
a. If the same, you are done.
b. If not the same, repeat step 3.
Sample Conversion Problems
1. How many grams are in 47.2 mg?
2. Change 702 cL to µL.
Step 1. Write down the number and unit.
47.2 mg
Sample Conversion Problems
1. How many grams are in 47.2 mg?
2. Change 702 cL to µL.
Step 1. Write down the number and unit.
47.2 mg
Step 2. Draw lines
47.2 mg
Sample Conversion Problems
1. How many grams are in 47.2 mg?
2. Change 702 cL to µL.
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
Sample Conversion Problems
1. How many grams are in 47.2 mg?
2. Change 702 cL to µL.
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
Sample Conversion Problems
1. How many grams are in 47.2 mg?
2. Change 702 cL to µL.
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.
Sample Conversion Problems
1. How many grams are in 47.2 mg?
2. Change 702 cL to µL.
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.
Sample Conversion Problems
1. How many grams are in 47.2 mg?
2. Change 702 cL to µL.
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.
Sample Conversion Problems
1. How many grams are in 47.2 mg?
2. Change 702 cL to µL.
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
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.
702 cL
Sample Conversion Problems
1. How many grams are in 47.2 mg?
2. Change 702 cL to µL. 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
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.
702 cL
Sample Conversion Problems
1. How many grams are in 47.2 mg?
2. Change 702 cL to µL. It’s 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
10-2 L 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.
702 cL
Sample Conversion Problems
1. How many grams are in 47.2 mg?
2. Change 702 cL to µL. It’s 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
702 cL
10-2 L μL
cL
10-6 L
= 7.02 x 106 μL
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.
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
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
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
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
3
lb
10 g
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
3
lb
10 g
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.
ROUNDING
When measurements are combined to provide
information, can the calculated result be of a higher
quality than the measurements?
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.
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.
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.
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.
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
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
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
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
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.
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.
Scientific Notation
1.
2.
3.
Place a decimal to the right of the
first nonzero number.
Place “X10” to the right of the
decimal number.
Count from the old decimal to the
new decimal. This number becomes
the power of 10; negative power, if
the number is less than one (if
number starts with zero, then it is
less than one)
Scientific Notation Examples
Convert the following into scientific notation.
a. 454,000 mi
Scientific Notation Examples
Convert the following into scientific notation.
a. 454,000 mi = 4.54
Step 1, place a decimal to the right of the first
non-zero number.
Scientific Notation Examples
Convert the following into scientific notation.
a. 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.
Scientific Notation Examples
Convert the following into scientific notation.
a. 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.
Scientific Notation Examples
Convert the following into scientific notation.
a. 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
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.
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
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
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
2.83 X 10-3 mi the same number of significant figures as
the starting measurement
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?
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?
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.
DENSITY UNITS
g/ml, g/cm3, (for solids and liquids), or
g/L for gases
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 it’s
the volume of the container !
DENSITY PROBLEM SOLVING STRATEGY
Use the four step unit analysis method from yesterday.
Organize the measurements to give density units.
Sample Problems
1. Calculate the density of a 4.07 g sample of rock that
displaces 1.22 mL of water.
2. Calculate the density of a 4.22 g sample of wood that
measures 2.0 cm by 1.33 cm by 3.56 cm.
3. Mercury has a density of 13.6 g/mL. Find the mass of 125
mL of mercury.
4. Water has a density of 1.00 g/mL. Find the volume, in
liters, of a 3.22 kg sample of water.
5. What does an object do in water with
a. A density greater than water?
b. A density less than water?
c. A density equal to water?
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
part X 100
total
form of:
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
105 X 100 = 35

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?
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
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
The End