DIMENSIONAL ANALYSIS AND CONVERSION OF METRIC UNITS

ANSONIA HIGH SCHOOL
20 Pulaski Highway  Ansonia, CT 06401
(203) 736.5060  fax (203) 736.5068
Rebecca Seibert
Advanced Placement/UCONN Chem 1127-1128
Chemistry Teacher
AP CHEMISTRY / UCONN ECE
Chemistry 1127 and 1128
Hi Everyone!
Welcome to Advanced Placement Chemistry and UCONN (8 credits!) Chemistry 1127 and
1128! This course is different from other chemistry classes. Rather than memorizing how to do
particular types of problems, you must really understand the chemistry, apply critical thinking skills
through writing and using mathematical skills to apply to different situations. To succeed, you must
keep up with the rigor and pace of the assignments, and be willing to spend significant time outside
of class working through the material.
1. Summer Assignment
I imagine that starting academic work for AP Chemistry is not high on your list of things to
do this summer! But, like many AP classes, AP Chem comes with a summer assignment. It is due
the first day of class and will be your first graded assignment for the year. The summer
assignments accounts for approximately 25% of your first quarter grade. You will be
tested on this material within the first week of school. The assignment is explained on the
next page.
2. Supplies
Please come to class the first day of school with the following supplies:
 3 to 4” three ring binder with notebook paper and dividers for class
 TI-Nspire graphing calculator or TI-84 type programmable scientific calculator (calculators
are used every day)
3. Laboratory Needs
You will be doing laboratory work your first week of school. Closed toe shoes, hair secured back
and safety glasses are required on lab days. A safety contract will be signed the first day of class.
Have a safe and happy summer. If you have any questions at all, you can contact me at
[email protected]. I look forward to having you in class next year!
Mrs. S
ANSONIA HIGH SCHOOL
20 Pulaski Highway  Ansonia, CT 06401
(203) 736.5060  fax (203) 736.5068
Rebecca Seibert
Advanced Placement Chemistry Teacher
AP CHEMISTRY SUMMER ASSIGNMENT
Part 1: Join Google Classroom: code 7h1dbqx
Part 2: Please contact me at this email ([email protected]) before the end of June to introduce
yourself and provide me your email. This is worth 10 points in the gradebook.
Misplace the summer assignment? It is on the school website and also Google Classroom.
Part 3: NMSI AP Chemistry Chemical Foundations packet:
 Read and complete the problems while watching the Companion video:
http://vimeo.com/14216778
 Password = linuspauling
o This video is one hour and five minutes long. The speaker talks through the Chemical
Foundations packet and works through several of the problems in the packet. This video
guides you through the packet and can be paused as you personally work the problems
in the packet.
 The packet and link to the video is available online (in case you misplaced yours):
http://apchemistrynmsi.wikispaces.com then look for the chemical foundations section
Part 4: Text: Chang, Raymond. Chemistry, 10th edition, McGraw Hill, 2010.


Read chapter 1, sections 1.1-1.9, and chapter 2 through p. 58.
o You are responsible for this content. Take notes. The Key Equations, Key Concepts and
Key Words are important to know. Taking notes on the chapter will help this process.
o You must show ALL work in a neat and organized manner for credit.
As you read, work all blue box Examples and the Practice Exercise at the bottom of each blue
box. The first two can be found on page 19. Answers for the practice exercises are at the back of
the chapter. Chapter 1 has eight in total; chapter two through page 58 has four.

Chapter 1 problems: 1.21, 1.22, 1.23, 1.25,1.29, 1.30, 1.33, 1.38, 1.39 (be careful: part d has
cubed units), 1.54, 1.61, 1.62

Chapter 2: 2.13, 2.14, 2.16, 2.17, 2.18, 2.27, 2.28, 2.33, 2.35, 2.36, 2.69, 2.70, 2.75
Part 5: Dimensional analysis (Yes, Math!)
 Complete the Dimensional Analysis and Conversions Packet, using the “train track or t-chart unit
cancellation” method outlined in the tutorial.

DIMENSIONAL ANALYSIS AND CONVERSION OF UNITS WORKSHEET
This worksheet is intended to show you a useful technique that can simplify your methods of answering conversion
problems.
It is important to use a systematic approach with easier problems so that when more difficult problems are
encountered, the method of approach itself does not add to the problem's difficulty.
In algebra you learned that if a quantity is multiplied by one, its value does not change. The number one can be
thought of as a quantity divided by its equivalent.
EXAMPLE: 1 year = 365 days is an equivalency statement and so are the following statements:
1 hour = 60 minutes
1 minute = 60 seconds
24 hours = 1 day
To solve the following problem you will need to use the statements above.
How many seconds are there in 5 years?
5 years
X
365 days
1 year
X
24 hr
1 day
X
The question is 5 years = ? seconds
0 min
X
1 hr
60 seconds
1 min
=
1.577 x 108 seconds
This is an equivalence statement (also called a conversion factor) and is equal to 1 so when you multiply it by
the original quantity you are not changing the size or value of the quantity but only changing the unit it is expressed
in. Notice that the top
and bottom units cancel each other and you are left with the final unit of seconds.
An easier way to write the above problem is shown below, especially when a long series of conversions is
needed
5 years
365 days
24 hr
60 min
1 year
1 day
1 hr
60 seconds
1 min
=
1.577 x 108 seconds
Mathematically you find the product of the top series of numbers and divided it by the product of the
bottom series of numbers. (Be sure to use parenthesis for the bottom #’s because you want to divide the
top quantity by the total bottom quantity)
We will also use this method to convert from one SI unit to another SI unit.
Suppose you wanted to convert the mass of a 250 mg aspirin tablet to its equivalent in grams. Start with what
you know and let the conversion factor units decide how to set up the problem. If a unit to be converted is in
the numerator, that unit must be in the denominator of the conversion factor to cancel.
Notice how the units cancel to give the unit grams.
Next, lets try a more involved conversion. Suppose you wanted to convert 250 mg to kg. You may or may not
know a direct, one-step conversion. In fact, the better method (fool proof) to do the conversion would be to go
to the base unit first, and then to the final unit you want. In other words, convert the milligrams to grams and
then to kilograms:
= 2.50 x 10-4 kg
Another EXAMPLE
The diameter of an argon atom is 3.0 x 10 -8 cm. How many of these atoms placed side by side in a straight line
would extend a length of 6.0 feet? (1 inch = 2.54 cm) The questions is 6.0 ft. = ? argon atoms
1 argon atom = 3.0 x 10 -8 cm
1 inch = 2.54 cm
12 in. = 1 ft.
6.0 ft
12 in
1 ft.
2.54 cm
1 in.
1 Ar atom
8.0 x 10 -8 cm
=
2.29 x 10 9 atoms
Another EXAMPLE
Three onions weigh 1.5 lb. and the price of onions is $ .11 per lb. What is the cost of six onions?
1. Question: 6 onions = ? $
2. Conversion factors: 3 onions = 1.5 lb and 1 lb = $ 0.11
3. Given information: 6 onions to start the set up
4. Set and place factors so that units cancel
6 onions
1.5 lb
3 onions
$0.11
1 lb
=
$0.33
Another EXAMPLE
The price of a ream of paper is $4.00. There are 500 sheets of paper in a ream. If a sheet of paper weighs 0.50 oz.,
what is the price of one pound of paper? (16 oz. = 1 lb)
1 lb paper = ? $
16 oz. = 1 lb 1 ream = $4.00
1 sheet = 0.50 oz.
1 lb
16 oz. 1 sheet
1 lb 0.50 oz.
500 sheets = 1 ream
1 ream
500 sheets
$4.00
1 ream
= _________
COMMON MISTAKES THAT STUDENTS MAKE IN SETTING UP THE PROBLEMS:
1. Setting up the conversion factors so that units will not cancel.
EX. 800,000,000 s x
60 s
1 min
seconds and min cannot cancel !!
2. Setting up units that cancel but the conversion factor is wrong.
EX. 800,000,000 s
(WRONG SOLUTION)
(WRONG SOLUTION)
x
60 min
1 second does not equal 60 min !!
1s
Make the following conversions using the method of dimensional analysis and show all
your work on separate paper.
Summary of STEPS FOR SOLVING WORD PROBLEMS USING DIMENSIONAL ANALYSIS:
1. Write the problem in the form of a question. What are you starting with? What are you solving
for?
2. List the possible equivalency statements or conversion factors (ratios)
3. Place the given information (What you are starting with) first in the set up.
4. Place the conversions so that the units that you want to get rid of are on opposite sides
(numerator and denominator) and will cancel.
5. When you are finished you should be left with the desired unit (what you are solving for).
6. To calculate the answer you will multiply across the top and divide by the product of the
bottom values.
7. Check to make sure that your answer is logical
Dimensional Analysis Worksheet
This worksheet is designed to give you practice using dimensional analysis as a problem solving tool. For
this reason it is very important to show your work. In each problem write the equality statement if you are
confused, if not then just write out the string of calculations with the correct conversion factor, including
the units. Show how the units cancel to give the final answer with the correct units. GOOD LUCK!!!
PART 1 Dimensional Analysis and the metric system. Memorize the prefixes of the metric system so
you can write the correct equivalence statements without assistance.
Prefix
Prefix
Abbreviation
Value
(Standard
Notation)
Value
(Scientific
Notation)
The math
ratio you
use!
(grams is the
unit used
here to
illustrate)
Kilo
Base unit
(grams,
liters,
meters)
K
1000
Times
larger
than the
base
103
deci
centi
milli
Micro
Nano
d
1/10
smaller
than the
base
c
1/100
smaller
than the
base
m
1/1000
smaller
than the
base
µ
1/1,000,000
smaller than
the base
n
1/1,000,000,000
smaller than the
base
100
10-1
10-2
10-3
10-6
10-9
1g
1g=
0.1 dg
1g=
0.01cg
1g=
0.001 mg
1g=
0.000001 µg
Or
1 g = 10-6 µg
1g=
0.000000001 ng
Or
1 g = 10-9 ng
1 this is
the base!
1 kg =
1000 g
1) Write an equivalence statement between the two given measurements.
A) 1 Km = ___________ m
or
1 m = _____________ Km
B) 1 µm = ___________m
or
1 m = _____________ µm
C) 1 mL = ____________L
or
1 L= ______________ mL
D) 1 nL = ____________mL
or
1 mL = ______________ nL
E) 1 ft = _____________ in
or
1 yard = ___________ ft
F) 1 cm = .39370
in
and
1 in = 2.54________cm
G) 1 km = .62137
mi
and
1 mi = 3.1117______ km
You are NOT required to memorize the conversion factors between the metric and English systems of
measurement.
2) Perform the following conversions using the equivalence statements you wrote in #1. SHOW YOUR
WORK IN THE SPACE PROVIDED UNDER EACH LETTER. WRITE SMALL!!
A) 75 Km = ? m
B) 2.68 x 10-6 µm = ? m
C) 11.2 nL = ? L
D) 37.687 yds = ? in
E) .00898 km = ? in
F) 8.98 x 1015 nm = ? mi
Part 2 Varied Applications
3) You visit the store and find a banana sale. On average 8 bananas weigh one pound. The sale price for
bananas is four pounds for $5.00. You decide to treat your advising group to 25 banana splits, 1 banana
per split.
A) Write the equivalence statements.
________________bananas = 1 lb
_______________lbs = _________________ dollars
B) How much will it cost you to buy 25 bananas?
4) The average length of a hotdog is 12.0 cm. The distance to the moon is 3.84 E8 meters. How many
hotdogs must you line up to reach the moon?
A) Write the equivalence statements
________ hot dog = _______ cm
__________ m = __________cm
distance to moon = __________________ m
B) How many hotdogs must you line up to reach the moon?
5) The distance to the sun is 1.496 E11 meters. The speed of light is 3.00 E8 m/s. A minute is defined to
be 60 seconds.
A Write the equivalence statements
Distance to sun = ________________ m
Speed of light = ____________________m/s
______________minute = _____________seconds
B) How long does it take for light to get from the sun to the earth?
6) If the density of mercury is 13.6 g/ml, find the A) mass of 43.0 ml of mercury, B) volume of 43.0
grams of mercury. (Hint: use the density of mercury to write an equivalence statement between mass and
volume.)
________________= ________________
A) Mass of 43.0 mL of mercury
B) Volume of 43.0 grams of mercury
7) You exhale about .0800 liters of CO2 (carbon dioxide) gas in a single breath. 22.4 liters of CO2 contain
6.022 x 1023 molecules. 6,022 x 1023 CO2 molecules have a mass of 44.0 grams. Find the A) number of
carbon dioxide molecules you exhale in each breath. Find the mass of the CO2 you exhale in a single
breath.
First, what ratio expressions do you know from the above information:
________________= ________________
________________= ________________
8) You have a salt shaker at home that contains 65.0 grams of NaCl. Table salt’s chemical formula is
NaCl and its name is sodium chloride. Chemists know that there are 58.44g NaCl in 1 mole of NaCl. A
mole is a measurement in chemistry, similar to the concept of 1 dozen contains 12 of something.
a) How many moles of NaCl are in your salt shaker?
b) If 1 mole = 6.02 x 1023 molecules of NaCl, how many molecules of NaCl are in your salt shaker?
DIMENSIONAL ANALYSIS PROBLEMS
Conversions Factors
1 hr = 60 min
1 min = 60 sec
1 ton = 2000 lbs
7 days = 1 week
24 hrs = 1 day
1 kg = 2.2 lbs
1 gal = 3.79 L
264.2 gal = 1 cubic meter
1 mi = 5,280 ft
1 kg = 1000 g
1 lb = 16 oz
20 drops = 1 mL
365 days = 1 yr
52 weeks = 1 yr
2.54 cm = 1 in
1 L = 1000 mL
0.621 mi = 1.00 km
1 yd = 36 inches
1 cc is 1 cm3
1 mL = 1 cm3
DIRECTIONS: Solve each problem using dimensional analysis. Every number must have a unit and be expressed
with proper significant figures and scientific notation. Work must be shown.
1. Convert 50 m to mm
2. Convert 25 cm to km
3. Convert 400 mm to m
4. Convert 60 kg to mg
5. Convert 500 nm to km
6. How many oranges are in a crate if the price of a crate of oranges is $1.60 and the price of
oranges is $0.20 per pound and there are 3 oranges per pound?
7. What is the cost to drive to Los Angeles from San Francisco a distance of 405 miles if the
cost of gasoline is $2.90 a gallon and the car gets 25 miles per gallon of gas?
8. What is the cost of coal in dollars per ton if it costs $0.04 per kilogram ?
9. If 6.0 liters of mercury has a mass of 78 kg and costs $420.00. What is the price of one
pound of mercury?
10.
If you dig a hole through the earth to China for a game of ping-pong , how many centuries
would it be before you got there if you could dig at a rate of 4 miles per day and the diameter
of the earth is 12,700 km?
11.
What would it cost to send a rocket to Mars, (7.9 x 10 7 km from the earth), if the average
speed of the rocket is 1600 miles per minute and the fuel consumption averages 100 grams
every 1.5 seconds and the cost of the fuel is $500.00 per pound ?
12.
You have been working at a fast food restaurant for the past 35 years wrapping
hamburgers. Each hour you wrap 184 hamburgers. You work 8 hours per day. You work 5
days a week. You get paid every 2 weeks with a salary of $840.34. How many hamburgers
will you have to wrap to make your first one million dollars?.
Lucky 13! (This is a UCONN test question!)
13.
The unit of land measure in the English system is the acre, while that in the metric system
is the hectare. An acre is 4.356x104 ft2. A hectare is ten thousand square meters. A town
requires a minimum area of 2.0 acres of land for 1 single-family dwelling. How many hectares
are required for one single family dwelling?