You may use a calculator.
Please use the Unit Analysis or Dimensional Analysis method to solve ONLY TWO of
the following word problems:
Back to Sample Back to Dimensional Analysis Main Menu
1. An oxygen molecule travels 975 mi/hr at room temperature. There are 5280 ft = 1 mi; 12 in = 1 ft, 2.54 cm = 1 in, 1.621 km = 1 mi, and 3600 sec = 1 hr. What is the velocity in meters per second?
____???____ m/sec = 975 mi/hr
1.
On the Numerator:
Change m to km to miles
or change m to cm to inches to feet to miles
2. then on the
denominator:
change hours to seconds or change
hours to minutes to seconds



??? m 
= 
975 mi 
X 
1.621 km 
X 
1000 m 
X 
1 hr 
= 
439 m 








1 sec 
1 hr 
1 mi 
1 km 
3600 sec 
1 sec 


2. If one gram is equal to 15.4 grains. How many 5.00 grain aspirin tablets may be made from 1.00 kilogram of aspirin?
____???_____ tab = 1.00 kg
Change kg to g to grains to tablets! (Three unit factors needed)



??? tab 
= 
1 kg 
X 
1000 g 
X 
15.4 grain 
X 
1 tab 
= 
3080 tab 








1 
1 
1 kg 
1 g 
5 grain 
1 


3. A parsec is the distance light travels in 3.26 years. Given the velocity of light, 3.00 x 10^{8} m/sec, how many kilometers does light travel in one parsec?
____???_____ km = 1 parsec
change parsec to years to
days to hours to minutes to seconds to meters then to kilometers



??? km 
= 
1 parsec 
X 
3.26 yr 
X 
365 day 
X 
24 hr 
X 
3600 sec 
X 
3.00 X 10^{8}
m 
= 
3.08 X 10^{13} km 










1 
1 
1 parsec 
1 yr 
1 day 
1 hr 
1 sec 
1 


4. I have 1400 radio programs I want to put on an Apple Ipod. Each program requires 5 megabytes of disk space. If there are 1024 megabytes in a gigabyte. How many gigabytes of disk space do I need minimum to store all my programs on the IPod. The MiniIpod holds only 4 gigabytes of recordings, could I use a mini for my project?
____???_____ Gb = 1400 programs
Change programs to megabytes to gigabytes



??? Gb 
= 
1400 Program 
X 
5 Mb 
X 
1 Gb 
= 
6.84 Gb 







1 
1 
1 Program 
1024 Mb 
1 


Problem#5
Find the mass in grains of a 325
milligram aspirin tablet.
(Given: 1.00 g = 15.4 grains)
____???_____ gr = 325 mg tablet
Change milligrams to grams to grains



??? gr 
= 
325 mg 
X 
1 g 
X 
15.4 gr 
= 
5.05 gr 







1 
1 
1000 mg 
1 g 
1 


Problem#6
Insurance statistics state that a person loses 8 minutes of average life for
each cigarette smoked. If there are 20 cigarettes in a pack and the average
cost of cigarette is $5.00 per pack over the next 25 years, how
many years of average life would a person lose for smoking 1.5 packs a day for 25 years?
____???____ yr_{lifelost} = 15 yr_{smoking}
Given Unit Factors

Unit Factors Not Given

Change years Smoking to Days Smoking to packs smoked to total cigarettes to minutes lost to hours lost to days lost to years lost
The important bridge between life lost and smoking is the 8
minutes _{lost} = 1 cig _{smoked} Unit Factor.



??? yr_{lifelost} 
= 
15 yr_{smok} 
X 
365 day_{smok} 
X 
1.5 pack 
X 
20 cig 
X 
8 min_{lost} 
X 
1 hr_{lost} 
X 
1 day_{lost} 
X 
1 yr_{lost} 
= 
2.5 yr_{lifelost}













1 
1 
1 yr_{smok} 
1 day_{smok} 
1 pack 
1 cig 
60 min_{lost} 
24 hr_{lost} 
365 day_{lost} 
1 


Problem7
What is the density of water in lb/ft^{3}, if the density of water at 25^{o}C is 1.00
g/ml?
[Hint: There are 2.54 cm = 1 in (or 16.48 cm^{3}
= 1 in^{3}); 454 g = 1 lb; 946 mL = 1 qt ]
____???_____ lb/ft^{3} = 1.00 g/mL
If you have different units to convert, you must do them separately:
First change the numerator unit (Grams) to the numerator answer (Pounds)
then
Second Change denominator unit to the denominator answer: Change mL to cm^{3} to in^{3} to ft^{3}

??? lb 
= 
1.00 g 
X 
1 lb 
X 
1 mL 
X 
16.48 cm^{3}

X 
1728 in^{3}

= 
62.4 lb 










1 ft^{3}

1 mL 
454 g 
1 cm^{3} 
1 in^{3}

1 ft^{3}

1 ft^{3}^{ } 
Problem#8
Calculate the velocity of a car traveling car traveling 65 miles/hr in
ft/sec.
__???___ ft/sec = 65 miles/hr
If you have different units to convert, you must do them separately:
First change the numerator unit (miles) to the numerator answer (feet) (one unit factor needed)
then
Second Change denominator unit (Hour) to the answer (Seconds) by: Change hr to min to sec (two unit factors needed)



??? gr 
= 
325 mg 
X 
1 g 
X 
15.4 gr 
= 
5.05 gr 







1 
1 
1000 mg 
1 g 
1 


Problem#9
How many milligrams does a 0.750
carat diamond weigh?
(Hint: 1 karat = 0.200 g)
____???____ mg = 0.750 carat
Given Unit Factors

Unit Factors Not Given




??? mg 
= 
0.750 carat 
X 
0.200 g 
X 
1000 mg 
= 
1.50 carat 







1 
1 
1 carat 
1 g 
1 


(#9a) How many karats is a diamond weighing
234.2 mg? (One karat = 0.200 g)
____???____ karat = 234.2 mg
Given Unit Factors

Unit Factors Not Given

Change mg to g then to carats (need two unit factors)



??? karat 
= 
234.2 mg 
X 
1 g 
X 
1 karat 
= 
1.17 karat 







1 
1 
1000 mg 
0.200 g 
1 


Problem#10
Diamond has a density of 3.513 g/cm^{3}. The mass of a diamond is often
measured in carats,
1 carat equaling 0.200 g. What is the volume of a 1.50 carat diamond?
____???____ cm^{3} = 1.50 carat
Given Unit Factors


Change carat to g then to cm^{3}
(need two unit factors)



??? cm^{3} 
= 
1.50 carat 
X 
0.200 g 
X 
1 cm^{3}

= 
0.0854 cm^{3} 







1 
1 
1 carat 
3.513 g 
1 


Problem#11
Liquor used to be sold in fifths. A fifth is one fifth of a gallon. A gallon is
128 fluid ounces. Today liquor is sold in bottle sizes of 750 ml to equate to
the old fifth. If there are 946 ml in a quart, calculate the number
of milliliters in a fifth. How many
milliliters difference is there in the
bottling?
____???____ mL = 1 fifth
Given Unit Factors

Unit Factors Not Given 4 quarts = 1 gallon 
Change fifths to gallons then to mL (need three unit factors)



??? mL 
= 
1 fifth 
X 
1 gal 
X 
4 qt 
X 
946 mL 
= 
756.8 mL 








1 
1 
5 fifths 
1 gal 
1 qt 
1 


How many milliliters difference is there in the bottling?
756.8 mL = 757 mL (three significant
figures)
757 mL – 750 mL = 7 mL difference
Problem #12
1. On
July 23, 1983 Air Canada Flight 143, flying at 26,000 feet from Montreal to
Edmonton, ran out of fuel because the first officer asked the mechanic for the
conversion factor of mass to volume at Montreal. The mechanic gave the first
officer the answer 1.77 with no units. The plane had 7682 L of fuel at Montreal.
The pilot knew he needed 22,300 kg of fuel to make the trip. The mechanic's
answer of 1.77 was pounds per liter not kilograms per liter caused the error
such that only 4917 L of fuel was added. If there are 2.205 pounds in a
kilogram, how many liters of fuel were needed for the trip? How
many liters minimum of fuel should have
been added at Montreal before takeoff?
____???____ L = 22,300 kg
Given Unit Factors

Unit Factors Not Given 
Change kg to pounds then to Liters (need two unit factors)



??? L 
= 
22,300 kg 
X 
2.205 lb 
X 
1 L 
= 
27,781 L 







1 
1 
1 kg 
1.77 lb 
1 


27,781
L (total needed) – 7682 L (in Tanks) = 20,099 L
(Needed to be added)
Problem #13
Before
1982 the US Mint cast penny coins from an alloy of copper and zinc. A 1980
Penny weighs 3.051 g and contains 2.898 g of pure copper. In 1982 the US Mint
stopped making copper pennies, because the price of copper was worth more than
the penny. The post 1982 penny contains only a layer of copper over zinc. A
1990 penny weighs 2.554 g and contains 2.490 g of zinc. If the mint melted down
one pound of 1980 pennies, how many 1990 pennies can be made from the total copper from the 1980
pennies?
Problems #14
An
Olympic size swimming pool is 50.0 m long and 25.0 m wide. How
many gallons of water (
d = 1.0g/mL )are needed to fill the pool to an
average depth of 5.5 feet.
Problem #15
A
furniture factory needs 29.5 ft^{2} of fabric to upholster one chair. A
European supplier sends the fabric in bolts of exactly 200 m^{2}. What
is the maximum number of chairs that can
be upholstered by three bolts of fabric. Hint: 1 m 
3.281 ft)?
Problem #16
My throw
away car gets 23.4 mi/gal and hold 70.1 L of gasoline. How
far can I drive on a tank full of gas?
If gas
cost $3.49/gal; how much does a tank full of gas cost?
If the
average speed on a trip is 92.2 km/hr, How many
hours may I drive the car on the trip before I run out of gas?
Additional Homework (not required) for your practice:
Corwin 7^{th} edition:
Page 59: #19 
#26