Unit 1: Relationships between Quantities and Reasoning with Equations
Lesson 2- Dimensional Analysis
How fast am I going?
20 mi per hour or
20 m per sec ?
Objectives:
 I can find the appropriate units for the solution to a problem.
 I can use conversion factors to perform dimensional
analysis.
 I can use dimensional analysis to solve real world problems.
Warm Up: Fill in the correct number to complete the conversion.
How many can you remember?
Length/Distance
_________ in = 1 ft
_________ ft = 1 yd
_________ ft = 1 mile
_________ mm = 1 cm
1 in = ______cm
1 mile = _____ km
Weight
________ oz = 1 lb
________ lbs = 1 ton
________ cg = 1 g
________ g = 1 kg
1 kg = _____ lbs
1 ton =_____ kg
Capacity/Volume
_____ oz = 1 cup
_____ cups = 1 pint
_____ pints = 1 quart
_____ quarts = 1 gallon
1 cup = _____ mL
1 gallon = _____ L
Dimensional Analysis:
In Lesson 1, we practiced converting units. Another name for this is
dimensional analysis. Dimensional analysis is a problem-solving
method that uses the fact that any number or expression can be
multiplied by one without changing its value. It is a useful technique.
It can aid in writing equations by determining how certain quantities
can be combined or used to solve word problems.
When solving a problem in order to combine
quantities, they must have the same units. It is also easier to
compare two quantities if they have the same units.
7cm + 1 in ≠ 8 cm or 8 in
You must convert one quantity so they have the same units.
7cm + 2.54 cm = 9.54 cm
Let’s try a few…
Jacob had a rope that was 3 feet long, Chad had a rope that was 72
inches long, and Tina had a rope that was 4 yards long. How much
rope do they have all together?
A police officer saw a car traveling 1,800 feet in 30 seconds. The
speed limit on that road is 55 miles per hour. Was the car speeding?
While traveling in Europe, Tanya noticed that price of gas was 1.4
pounds per liter. She wondered how that compares to the price of
gas back home. The exchange rate was 1 pound = $1.56. Find the
equivalent price in dollars per gallon.
You try!
A cupcake shop sells 14 dozen cupcakes on Monday, 32 cupcakes
on Tuesday, 65 cupcakes on Wednesday, 7 dozen cupcakes on
Thursday, and 12 dozen cupcakes on Friday. How many cupcakes
did they sell in all? (Hint: There are 12 units in a dozen.)
The speed limit is 65 miles per hour. You are traveling 2 km per
minute. Should you speed up or slow down to drive the speed limit?
Explain in words how you found your answer.
Ravi has started a business importing fabric from India. His supplier
charges him 460 rupees per meter for the fabric. He wants to make a
profit of $4 per yard. How much must Ravi charge per yard?
Use the following information to help you:
$1 = 57.3 rupees
1 m = 1.09 yards
Appropriate Units:
Can you think of a situation in which a quantity could
be given in pounds of vegetables per day?
*
*
When trying to find the answer to a word problem, many times we
can use the units for the final answer to help us get there.
Let’s try a few…
Dina took part in a diving completion. She dove 5 times, and her
scores were 8.8 points, 9.0 points, 8.6 points, 9.5 points, and 9.2
points. If she calculates her score on an average dive, in what units
should the answer be given?
A hospital’s records indicate that, on average, 23% of babies born
there are delivered by cesarean section. A total of 217 babies were
born at the hospital last year, and a total of 22 babies were born this
year. What should be the expected number of babies born by
cesarean section over both years?
Now you try!
The owner of a pool cleaning business wants to know how much
time, on average, his workers spend cleaning pools. Last week, 7
employees each worked a 6-hour shift. In all, the cleaned 42 pools.
What is the most appropriate units in which to calculate an answer to
his question?
A biologist notices that 14% of cows have two different colored eyes.
One farmer has 143 cows and another farmer has 167 cows. How
many cows would you expect to have two different colored eyes on
both farms?
According to an article in Runners' World magazine:
On average the human body is more than 50 percent water [by
weight]. Runners and other endurance athletes average around 60
percent. This equals about 120 soda cans' worth of water in a 160pound runner!
Investigate their calculation. Approximately how many soda cans’
worth of water are in the body of a 160-pound runner? What
unprovided information do you need to answer this question?
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While traveling in Scotland, Sandy noticed that the price of gas was
1.6 pounds per liter. She wondered how that compares to the price of gas in Akron,
where she lives. On that day, the exchange rate was 1 pound =$1.59. What would
the price in dollars per gallon be? (Use 1 L = 0.26 gal)
Name: _________________________
Unit 1 Lesson 2: Dimensional Analysis
1) Write an expression that converts 50 liters per minute into milliliters
per second.
2) Which is equivalent to 21.76
grams per minute?
a. 1.306 kg/h
b. 13.06 kg/h
c. 36.267 kg/h
d. 362.67 kg/h
3) Approximately 10% of people
are left-handed. Period 1 has 21
students, period 2 has 23
students, and period 3 has 19
students. How many students in
all would you expect to be lefthanded?
4) To qualify for a race, a runner must be able to run at a pace of at
least 15 kilometers per hour. Noah ran 5 miles in 30 minutes. Does
he qualify for the race?
Explain your answer.
5) In China, gas cost 95 Yuan per liter. Write an equivalent amount in
dollars per gallon. (Hint: 1 Yuan = $0.16 and 1 gallon = 3.79 L)
6) A team of scientists is studying the effects of a plant disease on a
forest. In a population of 100 trees, they found 12 of the trees
contracted the disease in one month. They need to predict the
effects of the disease over the next decade. What units should the
answer be given in?
7) Sadie has a cousin Nanette in Germany. Both families recently
bought new cars and the two girls are comparing how fuel-efficient
the two cars are. Sadie tells Nanette that her family’s car is getting 42
miles per gallon. Nanette has no idea how that compares to her
family’s car because in Germany mileage is measured differently.
She tells Sadie that her family’s car uses 6 liters per 100 km. Which
car is more fuel-efficient?