Transcript What is Dimensional Analysis?

What is Dimensional Analysis?
• Dimensional Analysis (also called
Factor-Label Method or the Unit Factor
Method) is a problem-solving method
that uses the fact that any number or
expression can be multiplied by one
without changing its value!
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Dimensional Analysis is not for
everyone. But it's probably for
you. First of all then, who
should avoid Dimensional
Analysis (DA)?
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Reasons for not using
Dimensional Analysis
1. Let's say you're super-intelligent and
enjoy solving relatively simple
problems in the most complex
manner.
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Reasons for not using
Dimensional Analysis
2. Let's say you're tired of always
getting the correct answers.
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Reasons for not using
Dimensional Analysis
• 3. Let's say you're an arty type and you
can't be confined by the structure of DA.
You like messy solutions scribbled all over
the page in every which direction. It's not
that you want to make a mistake, but you
really don't care that much about the
answer. You just like the abstract design
created by the free-wheeling solution... and
the freedom from being confined by
structure.
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Reasons for not using
Dimensional Analysis
4. Let's say that you have no interest in
going to the prom or making the
soccer team, and you don't mind
being unpopular, unattractive,
ignorant, insecure, uninformed, and
unpleasant.
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Otherwise,
You Need Dimensional
Analysis!
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Equalities
State the same measurement in two different
units
Example:
10.0 in.
25.4 cm
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Some Metric Equalities
Examples
Length
1m
=
100 cm
=
1000 g
=
1000 mL
Mass
1 kg
Volume
1L
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Some American Equalities
Examples
1 ft
=
12 inches
1 lb
=
16
1 quart
=
2 pints
1 quart
=
4 cups
oz
The quantities in each pair give the same
measured amount in two different units.
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Some Metric-American Equalities
Examples
1 in.
=
2.54 cm
1 qt
=
946 mL
1L
=
1.06 qt
1 lb
=
454 g
1 kg
=
2.20 lb
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Conversion Factors
An equality expressed as a fraction
ALWAYS EQUAL TO ONE!!!!!!!!!!
Example:
1 in. = 2.54 cm
Factors:
1 in.
2.54 cm
and
2.54 cm
1 in.
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Learning Check
Write conversion factors that relate each
of the following pairs of units:
We Do: Liters and mL
You Do: Hours and minutes
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Solution
A. Liters and mL
1L
and
1000 mL
1 L = 1000 mL
1000 mL
1L
B. hours and minutes
1 hr = 60 min
1 hr
and 60 min
60 min
1 hr
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Steps for solving problems• Write the number and unit you
are given.
2. Leave some space and write
= and the unit you are trying to
convert to.
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Steps for solving problems3. Use conversion factors that will
cancel out unwanted units until only
the unit you want is left.
4. Multiply all numbers on top.
Multiply all numbers on bottom.
Divide last.
5. Write final answer with units.
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I Do: How many inches are in 15.5 cm?
We Do: How many liters are in 6.50 moles?
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You Do: Express 24.0 cm in inches.
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You can also string many unit factors together:
I Do: A caterpillar is 3.45 cm long. How long is
the caterpillar in feet?
Unit Plan:
Solve:
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We Do: Sandra measured the length of a plant
and found that it was 13.2 cm long. How
long is this in yards?
Unit Plan:
Solve:
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You Do: Dave spent 30.5 minutes running
around his neighborhood. How much time
did he spend running in terms of years?
Unit Plan:
Solve:
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