Dimensional Analysis
Dimensional Analysis
Dimensional Analysis
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DIMENSIONAL ANALYSIS
WHAT IS DIMENSIONAL ANALYSIS?<br />
It is a method for solving conversion problems (relating<br />
one unit of measure to another).<br />
Conversion Factors are used to relate to measurements<br />
to each other.<br />
• They are either given to you or assumed to be known.<br />
• Example: 4 laps = 1 mile (these are equal to each other)<br />
Can be expressed as a fraction:<br />
• Since the numerator and denominator are equal, the fraction<br />
is equal to 1 and can be expressed either way.<br />
• You can convert laps into miles or miles into laps by<br />
multiplying by this conversion factor.
THE MATH BEHIND DIMENSIONAL<br />
ANALYSIS<br />
You are simply multiplying fractions for the<br />
purpose of cancelling out units.<br />
• Remember, anything that appears on the top and<br />
bottom of a fraction can be cancelled, even units!<br />
Example: To wash and dry a load of laundry will<br />
cost $2.75. The washing machine and dryer only<br />
take quarters. How many quarters will you need<br />
for one load of laundry?<br />
• Cancel out like terms, multiply everything on the top,<br />
multiply everything on the bottom, then divide.
SAMPLE DIMENSIONAL ANALYSIS PROBLEM<br />
Example: Convert 15 cm into meters.<br />
• Given: 15 cm<br />
• Find: length in meters<br />
• Conversion factor: 100 cm or 1m<br />
1 cm 100 cm<br />
• Solve: Given x Conversion factors = Find<br />
15 cm x 1 meter =<br />
100 cm<br />
.15 meters
DIMENSIONAL ANALYSIS<br />
SAMPLE PROBLEM #2<br />
•You're throwing a pizza party for 15 people. Each<br />
person might eat 4 slices. Each pizza will cost you<br />
$14.78 and will be cut into 12 slices. How much is the<br />
pizza going to cost you?<br />
Given x conversion factors<br />
= find<br />
15 people 4 slices 1 pizza $ 14.78<br />
1 people 12 slices 1 pizza<br />
= $73.90
Extra Credit: <strong>Dimensional</strong> <strong>Analysis</strong> Fun…<br />
from Lewis Caroll’s Through the looking Glass<br />
IF THERE ARE 5 FRUMIOUS BANDERSNATCHES,<br />
HOW MANY JABBERWOCKS ARE THERE?<br />
There are 20 tumtum trees in a tulgey wood.<br />
In each tulgey wood is one frumious Bandersnatch.<br />
There are 5 slithy toves in 2 borogoves.<br />
There are 2 mome raths per Jabberwock.<br />
There are 2 Jubjub birds in 200 tumtum trees.<br />
There are 200 mome raths in each borogove.<br />
There are 5 Jubjub birds per slithy tove.
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