Post on 03-Jan-2022
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Dimensional Analysis
Method
Follow along on your Dimensional
Analysis Worksheet and do the
example problem with the
presentation
2
Which is bigger?
• 120
• 5
• 21
Pennies
Quarters
Nickels
Answer = 5
The units are more important than the numbers!
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What is Dimensional Analysis?
• Dimension – means Unit
• Analysis – means Problem Solving
Math using units!
Use the units to find the solution to a
problem!
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What is Dimensional Analysis?
Dimensional analysis is
based on using “Conversion
Factors” to convert one type
of unit into another.
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What is a conversion factor?
• A conversion factor is an equality written as
a ratio.
• Every equality gives you two different
conversion factors.
cents 10 dime 1
1dime
cents 10r
cents 10
dime 1o
cents 10
dime 1
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What is a conversion factor?
• As a ratio of two equivalent terms, all
conversion factors equal 1.
Since 1 dime = 10 cents,
cents 10
dime 1the ratio
= 1
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How are conversion factors used?
When used correctly in a math problem, they allow us to convert from one type of unit to another!
cents 40 dime 1
cents 104dimes
Notice the unit, dime, cancels and we are left with cents!
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Setup
1. Write down given
2. Set up workspace
3. Write down units of answer
How many dimes are in 30 cents?
30 cents = dimes
This is the
single
step
example!
Step 2 Step 3
Step 1
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Solution
4. Do I want to keep it? If you don’t, write the unit on the bottom of the next line.
5. What can I change it into? Write that unit on top and then include the numbers.
6. Repeat until the answer to #4 is yes!
30 cents = dimes cents
dime 1
10 Step 4
Step 5
Step 6 – cents cancel and we
are left with dimes so “yes”
go to step 7
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Calculate
7. Everything on top is multiplied and everything on
the bottom is divided.
8. Plug the numbers in the calculator and let it do all
the work!
30 cents = dimes cents
dime 1
10
3 dimes )10(
)1)(30(Step 7
Step 8
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More info – Step 4
• Step 4 – Do I want to keep it?
– The it refers only to the unit. Don’t recopy the
number!
– The units are part of the calculation, so to
cancel a unit it must appear on the top and
bottom of a divisor.
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More info - Step 5
• Step 5 -What can I change it into?
– This really means “what do I know it equals”.
In the example, we wrote dime on top because
we know that 10 cents = 1 dime. We also know
100 cents = 1 dollar, but while we could write
dollar on top, it wouldn’t help us solve the
problem.
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More info – Step 5 continued
– In this step, you are finishing what you started
in step 4. You are actually completing what is
termed a “conversion factor” (a ratio of two
equivalent values). All conversion factors then
equal 1.
• 60 seconds = 1 minute can be written:
onds
uteor
ute
onds
sec60
min1
min1
sec60Both equal 1
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Homework
Use this technique to complete the
Dimensional Analysis worksheet!
Each problem is graded on the work –
NOT the answer. You are learning a
technique – show it if you want any
points!
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Multi-Step
Problems
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= 17.8 cm
km cm
m
100
1
m
km
1000
1 .000178
A pencil is 17.8 cm long. What is its length in km?
Two step metric conversions
(prefix unit to a prefix unit)
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Other Multi-Step Problems
= 2.5 wks s
wks
days
1
7
days
hours
1
24
hours
min
1
60 1512000
min
s
1
60
1500000 s
How many seconds are in 2.5 weeks?
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Complex
Dimensional
Analysis
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1. Square and Cubic unit conversions
= 3 cm3
m3 cm
m
100
1
cm
m
100
1
cm
m
100
1 .000003
Or
3 10-6 m3
How many m3 are in 3 cm3?
cm•cm•cm
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2. Complex Units (the hidden equality)
What does 60 mi/hr (this is a complex unit) really mean?
60 miles = 1 hr
1hr
60miles
60miles
1hror
It is a bridge to convert time and distance units!
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2. Complex Units
a. Using as a conversion factor
The density of gold is 19.3 g/mL. What is the mass if the
volume is 244.8 L?
= 244.8 L
g L
mL
1
1000
mL
g
1
19.3 4.72 106
19.3 g = 1 mL
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2. Complex Units b. Using as a given
The density of gold is 19.3 g/mL, what is it in cg/kL?
=
19.3 g = 1 mL
cg
kL
19.3 g
1 mL g
cg 100
1
mL
L
1000
1
L
kL
1000
1
1.93 109