2. A Little
About Me
• Grew up in Roswell, GA
• Attended Prep school in
Tennessee
• Coached lacrosse for 6+
years
• Previously taught
mathematics, statistics, and
psychology courses
3. Topics
• Units of Measure Review
• Scientific Notation Review
• Significant Figures
• Intro to Dimensional Analysis
6. Scientific Notation
Scientific notation is used to write very large or very small numbers such as
• the width of a human hair,
0.000008 m, which is also
written as 8 × 10−6
m
• the number of hairs on a
human scalp,100000,
which is also written as 1 × 105
hairs
33. Dimensional Analysis
• Is the chemist’s way of working chemistry problems that are mathematical in nature.
• Some memorization is vital to the method
• Learning the method saves time
34. Dimensional Analysis And
Conversions
• Metric conversions are all based on factors of 10 and prefixes.
• Metric System: know the required prefixes, meanings and
values for any base unit of measure
You are asked to memorize one particular way
Base Unit: gram Abbreviation: g
1 kg = 1000g
1 g = 10 dg = 100 cg = 1000 mg = 1x106
µg = 1x109
ng
35. Basis For Dimensional Analysis: ONE
• Multiplying by one does not change a value
• More than one way to multiply by one!
• What is =?
• =1
• What about if a = b…what is =?
• =1 AND =1
• So you can multiply something by an equality fraction and not change the innate value
36. 1. Read the question to figure out what you have/know for information. The question will provide you
with information that identifies your starting point and your final destination.
• Starting point = the number and unit provided by the question
• Final destination = the units desired after converting
2. Using the information gathered from the question, write your starting point and your final destination.
3. Determine the means in which you will get from your starting point to your final destination (simply
find “connections” or conversion factors between your starting and final unit).
4. Create a fraction by placing your starting point over one.
5. Multiply between fractions.
6. Write in the bottom unit of the new fraction. This should be the same as the top unit of the previous
fraction.
7. Write one set of “connections” or conversion factors into the fraction. Your bottom unit will guide
you.
8. Ask yourself, “Do I have the desired unit (final destination) on the top of the new fraction?”
NO YES
9. Cancel any units that are diagonal. (This should leave you with only the units that represent your final
destination)
10. Multiply the top of the fractions…multiply the bottom of the fractions…divide the top by the bottom.
US CONVERSION STEPS
(DIMENSIONAL ANALYSIS)
(Go back to step 5) (Proceed to step 9)
37. HOW MANY SECONDS ARE IN 6 MINUTES?
6 minutes seconds
(6 minutes)
1
( )
( )
seconds
minute
360 seconds
60
1
=
(6)(60 seconds)
(1)(1)
=
Step 1 – Read the question and determine
what information it provides you with
(starting point & final destination) Step 2 – Write down your
starting point and your final
destination
1 minute = 60 seconds
Step 3 –
Determine how
you will get
from your
starting point to
your final
destination (list
any
“connections” or
conversion
factors)
Step 4 – Create a fraction by
placing your starting point over
one
Step 5 – Multiply
between fractions
Step 6 – Write in the bottom unit
of the new fraction (this is the
same as the top unit of your
previous fraction)
Step 7 – Write the appropriate
conversion factor into the
fraction. Your bottom unit will
guide you.
Step 8 – Determine if this top
unit is the desired unit (your final
destination). In this case the
answer is YES, so we move on to
step 9
Step 9 – Cancel all diagonal units.
Once this is done, your final
destination should be the only
unit left – in this case seconds
Step 10 – Multiply the top of the
fractions; multiply the bottom of
the fractions; divide the product
of the top by the product of the
bottom
Starting Point
Final Destination
38. HOW MANY CENTIMETERS ARE IN 27
INCHES?
27 inches centimeters
(27 inches)
1
( )
( )
cm
inch
68.58 centimeters
2.54
1
= (27)(2.54 cm)
(1)(1)
=
Step 1 – Read the question and determine
what information it provides you with
(starting point & final destination) Step 2 – Write down your
starting point and your final
destination
1 inch = 2.54 centimeters
Step 3 –
Determine how
you will get
from your
starting point
to your final
destination (list
any
“connections”
or conversion
factors)
Step 4 – Create a fraction by
placing your starting point over
one
Step 5 – Multiply
between fractions
Step 6 – Write in the bottom unit
of the new fraction (this is the
same as the top unit of your
previous fraction)
Step 7 – Write the appropriate
conversion factor into the
fraction. Your bottom unit will
guide you.
Step 8 – Determine if this top
unit is the desired unit (your final
destination). In this case the
answer is YES, so we move on to
step 9
Step 9 – Cancel all diagonal units.
Once this is done, your final
destination should be the only
unit left – in this case
centimeters
Step 10 – Multiply the top of the
fractions; multiply the bottom of
the fractions; divide the product
of the top by the product of the
bottom
Starting Point
Final Destination
39. STUDENTS GO TO SCHOOL FOR 180 DAYS. HOW
MANY MINUTES IS THIS EQUAL TO?
180 days minutes
(180 days)
1
( )
( )
hours
day
259,200 minutes
24
1
=
(180)(24)(60 minutes)
(1)(1)(1) =
Step 1 – Read the question and determine
what information it provides you with
(starting point & final destination) Step 2 – Write down your
starting point and your final
destination
1 day = 24 hours
1 hour = 60 minutes
Step 3 –
Determine how
you will get
from your
starting point to
your final
destination (list
any
“connections” or
conversion
factors)
Step 4 – Create a fraction by
placing your starting point over
one
Step 5 – Multiply
between fractions
Step 6 – Write in the bottom unit
of the new fraction (this is the
same as the top unit of your
previous fraction)
Step 7 – Write the appropriate
conversion factor into the
fraction. Your bottom unit will
guide you.
Step 8 – Determine if this top
unit is the desired unit (your final
destination). In this case the
answer is NO, so we move back
to step 5
Step 9 – Cancel all diagonal units.
Once this is done, your final
destination should be the only unit
left – in this case minutes
Step 10 – Multiply the top of
the fractions; multiply the
bottom of the fractions;
divide the product of the top
by the product of the
bottom
Starting Point
Final Destination
( )
( )
minutes
hour
60
1
Step 5 – Multiply
between fractions
Step 6 – Write in the bottom unit
of the new fraction (this is the
same as the top unit of your
previous fraction)
Step 7 – Write the appropriate
conversion factor into the
fraction. Your bottom unit will
guide you.
Step 8 – Determine if this top
unit is the desired unit (your final
destination). In this case the
answer is YES, so we move on to
step 9
40. PRACTICE CONVERSIONS
1. How many seconds are in 6 minutes?
360 seconds
2. How many centimeters are in 27 inches?
68.58 centimeters
3. If a truck weighs 15,356 pounds, how many tons is it?
7.678 tons
4. If you had 10.5 gallons of milk, how many pints would you have?
84 pints
5. Students go to school for 180 days. How many minutes is this
equal to?
259,200 minutes
