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Chapter 1: Scientists’ Tools
Chemistry is an Experimental Science
This chapter will introduce the following
tools that scientists use to “do chemistry”
Section 1.1: Scientific Processes
Section 1.2: Observations & Measurements
Section 1.3: Designing Labs
Section 1.4: Converting Units
Section 1.5: Significant digits
Section 1.6: Scientific Notation
Chemistry is an Experimental Science
Although no
one method,
there are
Are used
when you
Design your
own labs
Common
characteristics
Unit
conversions
May require
include
Careful
observation
s
Accurate &
precise
measurements
Scientific
Notation
May require using
When using in
calculations, follow
Significant
digit rules
Section 1.1—Doing Science
There is no “The Scientific Method”
 There is no 1 scientific method with “X” number
of steps
 There are common processes that scientists use
Questioning & Observing
Gathering Data
 Experimentation
 Field Studies
 Long-term observations
 Surveys
 Literature reviews
 & more
Analyzing all the data
Using evidence & logic to draw conclusions
Communicating findings
Science is “loopy”
Observations
Questions
Data gathering
Hypothesis
Product or
technology
formation
(experiment, literature
research, field observations,
long-term studies, etc.)
Trend and pattern
recognition
Conclusion
formation
Communication &
Validation
Science is not a
linear
process…rather it
is “loopy”…and it’s
not just about
experimentation
…there are many
pathways…even
more than are
shown here!
Model Formation
Two types of Experiments
This text will predominantly use
experimentation for data gathering
Two types of experiments will be used:
To investigate relationships or effect
How does volume affect pressure?
How does reaction rate change with temperature?
To determine a specific value
What is the value of the gas law constant?
What is the concentration of that salt solution?
Variables
depends on
Example:
How does
reaction
rate change
with
temperatur
e
Independent Variable
Dependent Variable
Controlled by you
You measure or
observe
Variables
depends on
Example:
How does
reaction
rate change
with
temperatur
e
Independent Variable
Dependent Variable
Controlled by you
You measure or
observe
Temperature
Reaction rate
Variables
Independent Variable
Example:
What is the
concentratio
n of that salt
solution?
Dependent Variable
Variables
Variables are not appropriate in specific
value experiments
Independent Variable
Example:
What is the
concentratio
n of that salt
solution?
Dependent Variable
Not appropriate
Constants
It’s important to hold all variables other
than the independent and dependent
constant so that you can determine what
actually caused the change!
Constants
Example:
How does
reaction
rate change
with
temperatur
e
Constants
It’s important to hold all variables other
than the independent and dependent
constant so that you can determine what
actually caused the change!
Constants
Example:
How does
reaction
rate change
with
temperatur
e
Concentrations of
reactants
Volumes of
reactants
Method of
determining rate of
reaction
And maybe you thought of
some others!
Prediction versus Hypothesis
They are different!
Example:
How does
surface
area affect
reaction
rate?
Prediction
Hypothesis
Just predicts
Attempts to explain why
you made that prediction
Prediction versus Hypothesis
They are different!
Example:
How does
surface
area affect
reaction
rate?
Prediction
Hypothesis
Just predicts
Attempts to explain why
you made that prediction
Reaction rate will
increase as surface
area increases
Reaction rate will
increase with surface
area because more
molecules can have
successful collisions at
the same time if more
can come in contact
with each other.
Predictions versus Hypothesis
Prediction
Example:
What is the
concentratio
n of that salt
solution?
Hypothesis
Predictions versus Hypothesis
It is not appropriate to make a hypothesis
or prediction in specific value experiments
Prediction
Example:
What is the
concentratio
n of that salt
solution?
Hypothesis
Not appropriate—it would just be a random guess
Gathering Data
 Multiple trials help ensure that you’re results
weren’t a one-time fluke!
 Precise—getting consistent data within
experimental error
 Accurate—getting the “correct” or “accepted”
answer consistently
Example:
Describe
each group’s
data as not
precise,
precise or
accurate
Correct value
Correct value
Correct value
Precise & Accurate Data
Example:
Describe
each group’s
data as not
precise,
precise or
accurate
Correct value
Precise, but
not accurate
Correct value
Precise &
Accurate
Not precise
Correct value
Can you be accurate without precise?
This group had one value that was almost
right on…but can we say they were
accurate?
Correct value
Can you be accurate without precise?
This group had one value that was almost
right on…but can we say they were
accurate?
Correct value
No…they weren’t consistently correct. It was
by random chance that they had a result
close to the correct answer.
“Within Experimental Error”
 Precise is consistent within experimental error.
What does that mean?
 Every measurement has some error in it…we
can’t measure things perfectly. You won’t get
exactly identical results each time.
You have to decide if the variance in
your results is within acceptable
experimental error
Correct value
Drawing Conclusions
 Scientists take into account all the evidence from
the data gathering and draw logical conclusions
 Conclusions can support or not support earlier
hypothesis
 Conclusions can lead to new hypothesis, which
can lead to new investigations
 As evidence builds for conclusions, theories and
laws can be formed.
Theory versus Law
 Many people do not understand the difference
between these two terms
Cannot ever become
Example:
The
relationship
between
pressure
and volume
Theory
Law
Describes why something
occurs
Describes or predicts what
happens (often
mathematical)
Theory versus Law
 Many people do not understand the difference
between these two terms
Cannot ever become
Example:
The
relationship
between
pressure
and volume
Theory
Law
Describes why something
occurs
Describes or predicts what
happens (often
mathematical)
Kinetic Molecular Theory—
as volume decreases, the
frequency of collisions with
the wall will increase & the
collisions are the
“pressure”
Boyle’s Law:
P1V1 = P2V2
Communicating Results
 Scientists share results with the scientific
community to:
Validate findings (see if others have similar results)
Add to the pool of knowledge
 Scientists use many ways to do this:
Presentations and posters at conference
Articles in journals
Online collaboration & discussions
Collaboration between separate groups working on
similar problems
Section 1.2—Observations &
Measurements
Taking Observations
Qualitative descriptions
Color
Texture
Formation of solids, liquids, gases
Heat changes
Anything else you observe
Clear versus Colorless
Words to describe transparency
Clear
Cloudy
Opaque
See-through
Parts are seethrough with solid
“cloud” in it
Cannot be seen
through at all
Colorless does not describe transparency
You can be clear & colored
You need to describe the color of the solution &
the cloud if it’s cloudy
(examples: blue solution & white cloud or colorless
solution and blue solid)
Clear versus Colorless
Cherry Kool-ade
Example:
Describe the
following in
terms of
transparency
words &
colors
Whole Milk
Water
Clear versus Colorless
Example:
Describe the
following in
terms of
transparency
words &
colors
Cherry Kool-ade
Clear & red
Whole Milk
Opaque & white
Water
Clear & Colorless
Gathering Data
 Quantitative measurements
 International System of Units (SI Units) are used
Unit
Instrument used
Kilogram (kg)
Balance
Volume (how much space
it takes up)
Liters (L)
Graduated cylinder
Temperature (how fast
the particles are moving)
Kelvin (K) or Celsius
(°C)
Thermometer
Length
Meters (m)
Meter stick
Time
Seconds (sec)
stopwatch
Energy
Joules (J)
(Measured indirectly)
Quantity
Mass (how much stuff is
there)
Uncertainty in Measurement
 Every measurement has a degree of uncertainty
 The last decimal you write down is an estimate
Write down a “5” if it’s in-between lines
Write down a “0” if it’s on the line
Example:
Read the
measurements
25 mL
25 mL
20
20
15
15
10
10
5 mL
5 mL
Remember:
Always read liquid
levels from the
bottom of the
meniscus (the bubble
at the top)
Uncertainty in Measurement
 Every measurement has a degree of uncertainty
 The last decimal you write down is an estimate
Write down a “5” if it’s in-between lines
Write down a “0” if it’s on the line
25 mL
Example:
Read the
measurements
20
15
10
5 mL
It’s inbetween
the 10 &
11 line
10.5 mL
25 mL
20
15
10
5 mL
It’s on the
12 line
12.0 mL
Uncertainty in Measurement
Example:
Read the
measurements
1
1
2
2
3
3
4
4
5
5
6
6
7
8
7
8
Uncertainty in Measurement
It’s right on the 4.3 line
Example:
Read the
measurements
1
4.30
2
3
4
5
6
7
8
7
8
It’s between the 3.8 & 3.9 line
3.85
1
2
3
4
5
6
Uncertainty in Measurement
 Choose the right instrument
If you need to measure out 5 mL, don’t choose the
graduated cylinder that can hold 100 mL. Use the 10 or
25 mL cylinder
 The smaller the measurement, the more an error
matters—use extra caution with small quantities
If you’re measuring 5 mL & you’re off by 1 mL, that’s a
20% error
If you’re measuring 100 mL & you’re off by 1 mL, that’s
only a 1% error
Section 1.3—Designing Your
Own Labs
Designing Labs
 This is not giving a “scientific method”…rather
it’s giving hints at how to stay focused on the
goal when designing a lab to allow you to write
them more efficiently
 It gives you a plan of attack, but you can adjust it
as you need for various labs
Identify the purpose, problem, question
 If variables are appropriate (relationship or effect
lab), identify them in the problem
Example of a purpose: To determine the effect of
temperature on pressure
 If variables are not appropriate, be as
descriptive as possible
Example of a question: What is the concentration of a
saturated NaCl solution at room temperature?
 You can phrase it as a purpose or question
 You should also identify any important constants
Gather Background Information
 The background information section is where
you put together all the different concepts you
know together to solve your problem or answer
your question
 It might contain:
Definitions
Known relationships
Equations
Write a hypothesis
 Only when appropriate—only in relationship or
effect labs
 After looking at all your background information,
make a hypothesis (prediction with explanation
for why you think so)
Set-up the Results/Calculations section
 Write any equations that you will need to solve
your problem or answer your questions.
 You won’t have numbers to plug in, but you can
set up the equations/calculations now.
Set-up the Data Table
 Go through the calculations you set up and make a data
table that asks for each quantity you’ll need
 Remember that some measurements must be taken
indirectly & you will need to take that into account:
For example, you can’t put a chemical directly on the
balance, so you’ll need the mass of the container
(beaker or weighing dish) and then the mass of the
container & chemical in your data table
 Your data table should not contain any calculated values
(even just subtracting out the mass of the beaker)…only
those you will actually measure with an instrument!
Write your Procedure
 Procedures should be:
 Clear, Concise, Numbered list of steps
 Repeatable by someone of your same level of
experience/education
 Go through your data table and write a procedure
step to measure each thing asked for in your data
table.
 If the data table includes masses or volumes of
chemicals, give an approximate amount in the
procedure
 Example: Add approximately 2 g of NaCl to the beaker.
Find exact mass & record.
Write your Materials List
 Go through your procedure and make a list of
each piece of equipment and chemical that
you’ll need
 Be sure to include how many of each type of
equipment and what approximate quantity of
chemical
You don’t need to specify the amount of water
needed!
Write your Safety Concerns
 Go through your procedure & materials list
and specify any safety concerns.
 Possibilities include:
Wear goggles (anytime you use glass or chemicals)
Use caution with glassware
Use caution with hot glassware or hot chemicals
Any cautions specific to a chemical you’re using
(your teacher will tell you these)
Report any spills, breaks or incidents to your
teacher immediately
Wear aprons or gloves, if necessary
Now you’re ready to do your lab!
 Begin performing your lab (after your teacher
checks it for safety, if necessary)
 If you need to make changes to your
procedure at any time (you realize it’s not
quite right)…that’s OK
Just make sure you change the written procedure
as well so that when you’re done, the written report
reflects what you actually did
 Record your data in the data table
 Complete the calculations you’ve set up
Write your Conclusion
 Restate the purpose
 Completely answer the purpose with your
results
 Address any earlier hypothesis…does your
evidence support or not support it?
If it does not support the hypothesis, propose a new
hypothesis
 Suggest possible sources of error
“human error” is not specific enough & “Calculations”
doesn’t count
Section 1.4—Converting Units
Converting Units
 Often, a measurement is more convenient in one
unit but is needed in another unit for
calculations.
 Dimensional Analysis is a method for converting
unit
You may have learned another method of converting units in
math or previous science classes…trust me…learn this one
now!
It will help you solve many other chemistry problems later in the
class!
Equivalents
Dimensional Analysis uses
equivalents…what are they?
1 foot = 12 inches
What happens if you put one on top of the
other?
1 foot
12 inches
Equivalents
Dimensional Analysis uses
equivalents…what are they?
1 foot = 12 inches
What happens if you put one on top of the
other?
1 foot
=1
12 inches
When you put two things that
are equal on top & on bottom,
they cancel out and equal 1
Dimensional Analysis
 Dimensional analysis is based on the idea that
you can multiply anything by 1 as many times as
you want and you won’t change the physical
meaning of the measurement!
27 inches 
1
= 27 inches
Dimensional Analysis
 Dimensional analysis is based on the idea that
you can multiply anything by 1 as many times as
you want and you won’t change the physical
meaning of the measurement!
27 inches 
27 inches 
1
= 27 inches
1 foot
= 2.25 feet
12 inches
Dimensional Analysis
 Dimensional analysis is based on the idea that
you can multiply anything by 1 as many times as
you want and you won’t change the physical
meaning of the measurement!
27 inches 
27 inches 
1
= 27 inches
1 foot
= 2.25 feet
12 inches
Same physical
meaning…it’s
the same
length either
way!
Remember…this equals “1”
Canceling
 Anything that is on the top and the bottom of an
expression will cancel
 When canceling units…just cancel the units…
27 inches 
1 foot
12 inches
Unless the numbers cancel as well!
12 inches 
1 foot
12 inches
Steps for using Dimensional Analysis
1
Write down your given information
2
Write down an answer blank and the
desired unit on the right side of the problem
space
3
Use equivalents to cancel unwanted unit
and get desired unit.
4
Calculate the answer…multiply across the
top & divide across the bottom of the
expression
Common Equivalents
1 ft
1 in
1 min
1 hr
1 quart (qt)
4 pints
1 pound (lb)
=
=
=
=
=
=
=
12 in
2.54 cm
60 s
3600 s
0.946 L
1 quart
454 g
Example #1
1
Write down your given information
Example:
How many
grams are
equal to
1.25
pounds?
1.25 lb
Example #1
2
Write down an answer blank and the
desired unit on the right side of the problem
space
Example:
How many
grams are
equal to
1.25
pounds?
1.25 lb
= ________ g
Example #1
3
Use equivalents to cancel unwanted unit
and get desired unit.
Example:
How many
grams are
equal to
1.25
pounds?
1.25 lb

454 g
= ________ g
1 lb
Put the unit on
bottom that you
want to cancel
out!
The equivalent with these 2 units is: 1 lb = 454 g
A tip is to arrange the units first and then fill in numbers later!
Example #1
4
Calculate the answer…multiply across the
top & divide across the bottom of the
expression
Example:
How many
grams are
equal to
1.25
pounds?
1.25 lb

454 g
568
= ________
g
1 lb
Enter into the calculator: 1.25  454  1
Metric Prefixes
 Metric prefixes can be used to form
equivalents as well
 First, you must know the common metric
prefixes used in chemistry
kilo- (k)
deci- (d)
centi- (c)
milli- (m)
micro- (μ)
nano (n)
=
=
=
=
=
=
1000
0.1
0.01
0.001
0.000001
0.000000001
These prefixes
work with any
base unit, such
as grams (g),
liters (L), meters
(m), seconds (s),
etc.
Metric Equivalents
 Many students confuse where to put the
number shown in the previous chart…it
always goes with the base unit (the one
without a prefix)
kilo = 1000
Example:
Write a
correct
equivalent
between
“kg” and “g”
There are two options:
1 kg = 1000 g
1000 kg = 1 g
To help you write correct equivalents, read the
number that equals the prefix as the prefix itself in
a “sentence”
Metric Equivalents
 Many students confuse where to put the
number shown in the previous chart…it
always goes with the base unit (the one
without a prefix)
kilo = 1000
Example:
Write a
correct
equivalent
between
“kg” and “g”
There are two options:
1 kg = 1000 g “1 kg is kilo-gram”…correct
1000 kg = 1 g “kilo- kg is 1 gram”…incorrect
To help you write correct equivalents, read the
number that equals the prefix as the prefix itself in
a “sentence”
Try More Metric Equivalents
Example:
Write a
correct
equivalent
between
“mL” and
“L”
Example:
Write a
correct
equivalent
between
“cm” and
“m”
milli = 0.001
There are two options:
1 L = 0.001 mL
0.001 L = 1 mL
centi = 0.01
There are two options:
1 cm = 0.01 m
0.01 cm = 1 m
Try More Metric Equivalents
Example:
Write a
correct
equivalent
between
“mL” and
“L”
Example:
Write a
correct
equivalent
between
“cm” and
“m”
milli = 0.001
There are two options:
1 L = 0.001 mL “1 L is milli-mL”…incorrect
0.001 L = 1 mL “milli-liter is 1 mL”…correct
centi = 0.01
There are two options:
1 cm = 0.01 m “1 cm is centi-meter”…correct
0.01 cm = 1 m “centi-cm is 1 m”…incorrect
Metric Volume Units
height
 To find the volume of a cube, measure each
side and calculate: length  width  height
length
 But most chemicals aren’t nice, neat cubes!
 Therefore, they defined 1 milliliter as equal to
1 cm3 (the volume of a cube with 1 cm as
each side measurement)
1 cm3
=
1 mL
Example #2
Example:
How many
grams are
equal to
127.0 mg?
127.0 mg
= ________ g
You want to convert between mg & g
“1 mg is 1 milli-g”
1 mg = 0.001 g
Example #2
Example:
How many
grams are
equal to
127.0 mg?
127.0 mg 
0.001 g
0.1270 g
= ________
1 mg
You want to convert between mg & g
“1 mg is 1 milli-g”
1 mg = 0.001 g
Enter into the calculator: 127.0  0.001  1
You may be able to do this in your head…but practice the technique
on the more simple problems so that you’ll be a dimensional
analysis pro for the more difficult problems (like stoichiometry)!
Multi-step problems
 There isn’t always an equivalent that goes
directly from where you are to where you want to
go!
 Rather than trying to determine a new
equivalent, it’s faster to use more than one step
in dimensional analysis!
 This way you have fewer equivalents to
remember and you’ll make mistakes more often
 With multi-step problems, it’s often best to plug
in units first, then go back and do numbers.
Example #3
Example:
How many
kilograms
are equal to
345 cg?
345 cg
= _______ kg
There is no equivalent between cg & kg
With metric units, you can always get to the base unit from any
prefix!
And you can always get to any prefix from the base unit!
You can go from “cg” to “g”
Then you can go from “g” to “kg”
Example #3
Example:
How many
kilograms
are equal to
345 cg?
345 cg 
g
cg

kg
= _______ kg
g
Go to the base unit
Go from the base unit
Example #3
Example:
How many
kilograms
are equal to
345 cg?
345 cg 
0.01 g
1 cg
1 cg = 0.01 g
1000 g = 1 kg

1 kg
= _______ kg
1000 g
Remember—the # goes with the
base unit & the “1” with the prefix!
Example #3
Example:
How many
kilograms
are equal to
345 cg?
345 cg 
0.01 g
1 cg

1 kg
0.00345 kg
= _______
1000 g
Enter into the calculator: 345  0.01  1  1  1000
Whenever dividing by more than 1 number, hit the divide key
before EACH number!
It doesn’t matter what order you type this in…you could multiply,
divide, multiply divide if you wanted to!
Let’s Practice #1
Example:
0.250 kg is
equal to
how many
grams?
Let’s Practice #1
Example:
0.250 kg is
equal to
how many
grams?
0.250 kg 
1000 g
1 kg
1 kg = 1000 g
Enter into the calculator: 0.250  1000  1
250. g
= ______
Let’s Practice #2
Example:
How many
mL is equal
to 2.78 L?
Let’s Practice #2
Example:
How many
mL is equal
to 2.78 L?
2.78 L 
1 mL
.001 L
1 mL = 0.001 L
Enter into the calculator: 2.78  1  0.001
2780 mL
= ______
Let’s Practice #3
Example:
147 cm3 is
equal to
how many
liters?
Let’s Practice #3
Remember—cm3 is a volume unit, not a length like meters!
Example:
147 cm3 is
equal to
how many
liters?
147
cm3

1 mL
1 cm3

0.001 L
1 mL
There isn’t one direct equivalent
1 cm3 = 1 mL
1 mL = 0.001 L
Enter into the calculator: 147  1  0.001  1  1
0.147 L
= _______
Let’s Practice #4
Example:
How many
milligrams
are equal to
0.275 kg?
Let’s Practice #4
Example:
How many
milligrams
are equal to
0.275 kg?
0.275 kg 
1000 g
1 kg

1 mg
275,000 mg
= _______
0.001 g
There isn’t one direct equivalent
1 kg = 1000 g
1 mg = 0.001 g
Enter into the calculator: 0.275  1000  1  1  0.001
Section 1.5—Significant Digits
Section 1.5 A
Counting significant digits
Taking & Using Measurements
 You learned in Section 1.3 how to take careful
measurements
 Most of the time, you will need to complete
calculations with those measurements to
understand your results
1.00 g
3.0 mL
= 0.3333333333333333333 g/mL
If the actual measurements were only
taken to 1 or 2 decimal places…
how can the answer be known
to and infinite number of
decimal places?
It can’t!
Significant Digits
A significant digit is anything that you
measured in the lab—it has physical
meaning
The real purpose of “significant digits” is to
know how many places to record in an
answer from a calculation
But before we can do this, we need to
learn how to count significant digits in a
measurement
Significant Digit Rules
1
All measured numbers are significant
2
All non-zero numbers are significant
3
Middle zeros are always significant
4
Trailing zeros are significant if there’s a
decimal place
5
Leading zeros are never significant
All the fuss about zeros
102.5 g
125.0 mL
Middle zeros are important…we know that’s a zero (as
opposed to being 112.5)…it was measured to be a zero
The convention is that if there are ending zeros with a
decimal place, the zeros were measured and it’s
indicating how precise the measurement was.
125.0 is between 124.9 and 125.1
125 is between 124 and 126
0.0127 m
The leading zeros will dissapear if the units are
changed without affecting the physical meaning or
precision…therefore they are not significant
0.0127 m is the same as 127 mm
Sum it up into 2 Rules
The 4 earlier rules can be summed up into 2 general rules
1
If there is no decimal point in the number,
count from the first non-zero number to the
last non-zero number
2
If there is a decimal point (anywhere in the
number), count from the first non-zero
number to the very end
Examples of Summary Rule 1
1
If there is no decimal point in the number,
count from the first non-zero number to the
last non-zero number
Example:
Count the
number of
significant
figures in
each
number
124
20570
200
150
Examples of Summary Rule 1
1
If there is no decimal point in the number,
count from the first non-zero number to the
last non-zero number
Example:
Count the
number of
significant
figures in
each
number
124
3 significant digits
20570
4 significant digits
200
1 significant digit
150
2 significant digits
Examples of Summary Rule 2
2
If there is a decimal point (anywhere in the
number), count from the first non-zero
number to the very end
Example:
Count the
number of
significant
figures in
each
number
0.00240
240.
370.0
0.02020
Examples of Summary Rule 2
2
If there is a decimal point (anywhere in the
number), count from the first non-zero
number to the very end
Example:
Count the
number of
significant
figures in
each
number
0.00240
3 significant digits
240.
3 significant digits
370.0
4 significant digits
0.02020
4 significant digits
Importance of Trailing Zeros
Just because the zero isn’t “significant”
doesn’t mean it’s not important and you
don’t have to write it!
“250 m” is not the same thing as “25 m” just
because the zero isn’t significant
The zero not being significant just tells us that it’s
a broader range…the real value of “250 m” is
between 240 m & 260 m.
“250. m” with the zero being significant tells us
the range is from 249 m to 251 m
Let’s Practice
Example:
Count the
number of
significant
figures in
each
number
1020 m
0.00205 g
100.0 m
10240 mL
10.320 g
Let’s Practice
Example:
Count the
number of
significant
figures in
each
number
1020 m
3 significant digits
0.00205 g
3 significant digits
100.0 m
4 significant digits
10240 mL
4 significant digits
10.320 g
5 significant digits
Section 1.5 B
Calculations with significant digits
Performing Calculations with Sig Digs
When recording a calculated answer, you can only be as
precise as your least precise measurement
1
Addition & Subtraction: Answer has least
number of decimal places as appears in the
problem
2
Multiplication & Division: Answer has least
number of significant figures as appears in
the problem
Always complete the calculations first, and
then round at the end!
Addition & Subtraction Example #1
1
Addition & Subtraction: Answer has least
number of decimal places as appears in the
problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
15.502 g
+ 1.25 g
16.752 g
This answer assumes the missing digit in the problem is a
zero…but we really don’t have any idea what it is
Addition & Subtraction Example #1
1
Addition & Subtraction: Answer has least
number of decimal places as appears in the
problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
15.502 g
+ 1.25 g
3 decimal places
Lowest is “2”
2 decimal places
16.752 g
Answer is
rounded to 2
decimal places
16.75 g
Addition & Subtraction Example #2
1
Addition & Subtraction: Answer has least
number of decimal places as appears in the
problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
10.25 mL
- 2.242 mL
8.008 mL
This answer assumes the missing digit in the problem is a
zero…but we really don’t have any idea what it is
Addition & Subtraction Example #2
1
Addition & Subtraction: Answer has least
number of decimal places as appears in the
problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
10.25 mL
- 2.242 mL
2 decimal places
Lowest is “2”
3 decimal places
8.008 mL
Answer is
rounded to 2
decimal places
8.01 mL
Multiplication & Division Example #1
2
Multiplication & Division: Answer has least
number of significant figures as appears in
the problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
10.25 g
2.7 mL
= 3.796296296 g/mL
Multiplication & Division Example #1
2
Multiplication & Division: Answer has least
number of significant figures as appears in
the problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
4 significant digits
Lowest is “2”
10.25 g
2.7 mL
= 3.796296296 g/mL
2 significant digits
Answer is
rounded to 2
sig digs
3.8 g/mL
Multiplication & Division Example #2
2
Multiplication & Division: Answer has least
number of significant figures as appears in
the problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
1.704 g/mL
 2.75 mL
4.686 g
Multiplication & Division Example #2
2
Multiplication & Division: Answer has least
number of significant figures as appears in
the problem
Example:
Compute &
write the
answer with
the correct
number of
sig digs
1.704 g/mL
 2.75 mL
4 significant dig
Lowest is “3”
3 significant dig
4.686 g
Answer is
rounded to 3
significant digits
4.69 g
Let’s Practice #1
Example:
Compute &
write the
answer with
the correct
number of
sig digs
0.045 g
+ 1.2 g
Let’s Practice #1
Example:
Compute &
write the
answer with
the correct
number of
sig digs
0.045 g
+ 1.2 g
3 decimal places
Lowest is “1”
1 decimal place
1.245 g
Answer is
rounded to 1
decimal place
1.2 g
Addition & Subtraction use number of decimal places!
Let’s Practice #2
Example:
Compute &
write the
answer with
the correct
number of
sig digs
2.5 g/mL
 23.5 mL
Let’s Practice #2
Example:
Compute &
write the
answer with
the correct
number of
sig digs
2.5 g/mL
 23.5 mL
2 significant dig
Lowest is “2”
3 significant dig
58.75 g
Answer is
rounded to 2
significant digits
59 g
Multiplication & Division use number of significant digits!
Let’s Practice #3
Example:
Compute &
write the
answer with
the correct
number of
sig digs
1.000 g
2.34 mL
Let’s Practice #3
Example:
Compute &
write the
answer with
the correct
number of
sig digs
4 significant digits
1.000 g
2.34 mL
Lowest is “3”
= 0.42735 g/mL
3 significant digits
Answer is
rounded to 3
sig digs
0.427 g/mL
Multiplication & Division use number of significant digits!
Section 1.6—Scientific
Notation
Scientific Notation
 Scientific Notation is a form of writing very large
or very small numbers that you’ve probably used
in science or math class before
 Scientific notation uses powers of 10 to shorten
the writing of a number.
Writing in Scientific Notation
The decimal point is put behind the first
non-zero number
The power of 10 is the number of times it
moved to get there
A number that began large (>1) has a
positive exponent & a number that began
small (<1) has a negative exponent
Example #1
12457.656 m
Example:
Write the
following
numbers in
scientific
notation.
0.000065423 g
128.90 g
0.0000007532 m
Example #1
Example:
Write the
following
numbers in
scientific
notation.
4
12457.656 m
1.24567656  10 m
0.000065423 g
6.5423  10 g
128.90 g
1.2890  10 m
-5
2
-7
0.0000007532 m 7.532  10 m
The decimal is moved to follow the first non-zero number
The power of 10 is the number of times it’s moved
Example #1
Example:
Write the
following
numbers in
scientific
notation.
4
12457.656 m
1.24567656  10 m
0.000065423 g
6.5423  10 g
128.90 g
1.2890  10 m
-5
2
-7
0.0000007532 m 7.532  10 m
Large original numbers have positive exponents
Tiny original numbers have negative exponents
Reading Scientific Notation
A positive power of ten means you need to
make the number bigger and a negative
power of ten means you need to make the
number smaller
Move the decimal place to make the
number bigger or smaller the number of
times of the power of ten
Example #2
1.37  104 m
Example:
Write out
the
following
numbers.
2.875  102 g
8.755  10-5 g
7.005 10-3 m
Example #2
Example:
Write out
the
following
numbers.
1.37  104 m
13700 m
2.875  102 g
287.5 g
8.755  10-5 g
0.00008755 m
7.005 10-3 m
0.007005 m
Move the decimal “the power of ten” times
Positive powers = big numbers. Negative powers = tiny numbers
Scientific Notation & Significant Digits
Scientific Notation is more than just a short
hand.
Sometimes there isn’t a way to write a
number with the needed number of
significant digits
…unless you use scientific notation!
Take a look at this…
Write 120004.25 m with 3 significant digits
120004.25 m
8 significant digits
120000. m
6 significant digits
120000 m
2 significant digits
1.20  105 m
3 significant digits
120. m
Remember…120 isn’t the same as 120000! Just because
those zero’s aren’t significant doesn’t mean they don’t
have to be there! This answer isn’t correct!
Examples #3
120347.25 g
Example:
Write the
following
numbers in
scientific
notation.
with 3 sig digs
0.0002307 m with 2 sig digs
12056.76 mL with 4 sig digs
0.00000024 g with 2 sig digs
Examples #3
120347.25 g
Example:
Write the
following
numbers in
scientific
notation.
with 3 sig digs
1.20 × 105 g
0.0002307 m with 2 sig digs
2.3 × 10-4 g
12056.76 mL with 4 sig digs
1.206 × 104 g
0.00000024 g with 2 sig digs
2.4 × 10-7 g
Move the decimal after the first non-zero number
Start counting significant figures from that first non-zero number
Round when you get the wanted number of significant digits
Remember—large numbers are positive powers of ten & tiny numbers have
negative powers of ten!
Let’s Practice
0.0007650 g
Example:
Write the
following
numbers in
scientific
notation.
with 2 sig digs
120009.2 m with 3 sig digs
239087.54 mL with 4 sig digs
0.0000078009 g with 3 sig digs
1.34 × 10-3 g
Example:
Write out
the
following
numbers
2.009  10-4 mL
3.987  105 g
2.897  103 m
Let’s Practice
0.0007650 g
Example:
Write the
following
numbers in
scientific
notation.
Example:
Write out
the
following
numbers
with 2 sig digs
7.7 × 10-4 g
120009.2 m with 3 sig digs
1.20 × 105 g
239087.54 mL with 4 sig digs
2.391 × 105 g
0.0000078009 g with 3 sig digs
7.80 × 10-6 g
1.34 × 10-3 g
0.00134 g
2.009  10-4 mL
0.0002009 mL
3.987  105 g
39870 g
2.897  103 m
2897 m
Chapter 1—Scientists’ Tools
Summary
Chemistry is an Experimental Science
 You have learned the following:
Common characteristics of scientific processes
How observations & measurements are taken
accurately & precisely during those scientific processes
How to design a lab yourself to answer questions
How to convert units you’ve measured in to ones that
are more useful to calculate with
How to report answers to calculations with the correct
number of significant digits to represent the accuracy of
the measurements you took in the lab
How to use scientific notation to express the correct
number of significant figures
What did you learn about
Scientists’ tools?
Chemistry is an Experimental Science
Although no
one method,
there are
Are used
when you
Design your
own labs
Common
characteristics
Unit
conversions
May require
include
Careful
observation
s
Accurate &
precise
measurements
Scientific
Notation
May require using
When using in
calculations, follow
Significant
digit rules