Chapter 5.6
Dimensional Analysis
Objective: Learn how to use dimensional
analysis to solve problems
Mrs. Baldessari
Chemistry
Conversion Problems
Because each country’s
currency compares
differently with the U.S.
dollar, knowing how to
convert currency units
correctly is very
important. Conversion
problems are readily
solved by a problemsolving approach called
dimensional analysis.
What is Dimensional Analysis?
Ex: 3 cm = 50 km
Since the map is a small-scale representation of a large area,
there is a scale that you can use to convert from small-scale
units to large-scale units—for example, going from inches to
miles or from cm to km.
What is Dimensional Analysis?
Whenever you use a map or exchange
currency, you are utilizing the scientific
method of dimensional analysis.
A conversion factor is a ratio of equivalent
measurements.
The ratios 100 cm/1 m and 1 m/100 cm are
examples of conversion factors.
When a measurement is multiplied by a conversion
factor, the numerical value is generally changed,
but the actual size of the quantity measured
remains the same.
Examples of Conversions
You can write any conversion as a
fraction.
Be careful how you write that fraction.
For example, you can write
1 m = 100cm
as 1m
100 cm
or
100 cm
1m
Examples of Conversions
Again, just be careful how you write the
fraction.
The fraction must be written so that like
units cancel.
For example. How many liters do you
have with 50 mL?
Steps
1. Start with the given value.
2. Write the multiplication symbol.
3. Choose the appropriate conversion factor.
4. The problem is solved by multiplying the
given data & their units by the appropriate
unit factors so that the desired units
remain.
5. Remember, cancel like units.
Let’s try some examples together…
1. Suppose there are 12 slices of pizza in
one pizza. How many slices are in 7
pizzas?
1.
2.
3.
Start with the given
value.
Write the
multiplication
symbol.
Choose the
appropriate
conversion factor.
Given: 7 pizzas
Want: # of slices
Conversion: 12 slices = one pizza
Solution
Check your work…
7 pizzas
1
X
12 slices
1 pizza
=
84 slices
Let’s try some examples together…
2.
How old are you in days?
Given: 17 years
Want: # of days
Conversion: 365 days = one year
Solution
Check your work…
17 years
1
X
365 days
1 year
=
6052 days
Let’s try some examples together…
3.
There are 2.54 cm in one inch. How
many inches are in 17.3 cm?
Given: 17.3 cm
Want: # of inches
Conversion: 2.54 cm = one inch
Solution
Check your work…
17.3 cm
1
X
1 inch
2.54 cm
=
6.81 inches
Be careful!!! The fraction bar means divide.
How many quarts is 9.3 cups?
9.3 cups
=
? quarts
9.3 cups
1
x
quart
9.3 x 1
=
4
cups
1 x 4
9.3
=
=
4
2.325
s
Now, you try…
1. Determine the number of eggs in 23
dozen eggs.
Answer: 276 eggs
Now, you try…
2. If one package of gum has 10 pieces,
how many pieces are in 0.023
packages of gum?
Answer: 0.23 pieces
Multiple-Step Problems
Most problems are not simple one-step
solutions. Sometimes, you will have to
perform multiple conversions.
Example: How old are you in hours?
Given: 17 years
Want: # of days
Conversion #1: 365 days = one year
Conversion #2: 24 hours = one day
Solution
Check your work…
17 years
1
X
365 days
1 year
X
24 hours
1 day
148,920 hours
=
Combination Units
Dimensional Analysis can also be used
for combination units.
Like converting km/h into cm/s.
Write the fraction in a “clean” manner:
km/h becomes km
h
Combination Units
Example: Convert 0.083 km/h into m/s.
Given: 0.083 km/h
Want: # m/s
Conversion #1: 1000 m = 1 km
Conversion #2: 1 hour = 60 minutes
Conversion #3: 1 minute = 60 seconds
Solution
Check your work…
0.083 km
1 hour
83 m
1 hour
X
1000 m
1 km
X
1 hour
60 min
=
X
0.023 m
sec
83 m
1 hour
1 min
60 sec
=
Section Quiz
1. 1 Mg = 1000 kg. Which of the following
would be a correct conversion factor for this
relationship?
 1000.
 1/1000.
÷ 1000.
1000 kg/1Mg.
Now, you try…
Complete your assignment by yourself.
If you have any questions, ask me as I
will be walking around the room.
The following slides provide more
worked examples for students who need
more practice.
Extra practice # 1
Extra practice # 1
Start with what value is known, proceed to the unknown.
Extra practice # 1
Extra practice # 1
Extra practice # 2
Extra practice #2
extra practice # 2
Extra practice # 2
Extra practice # 3
Extra practice # 3
Extra practice # 3
Extra practice # 3
Extra practice # 4
Hint: When converting between
units, it is often necessary to use
more than one conversion factor.
Extra practice # 4
Extra practice # 4
Extra practice # 4
Converting Between Units
Converting Complex Units
Many common measurements are
expressed as a ratio of two units. If you
use dimensional analysis, converting
these complex units is just as easy as
converting single units. It will just take
multiple steps to arrive at an answer.
Extra practice # 5
Extra practice # 5
Extra practice # 5
Extra practice # 5