have you ever been to a foreign country? one of the most important things to do when visiting...
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DIMENSIONAL ANALYSIS
What is Dimensional Analysis?
Have you ever been to a foreign country?
One of the most important things to do when visiting another country is to exchange currency.
For example, one United States dollar equals 1535.10 Lebanese Pounds.
What is Dimensional Analysis?
Whenever you exchange currency, you are utilizing the scientific method of dimensional analysis.
What is Dimensional Analysis?
Dimensional analysis is a problem-solving method that uses the idea that any number or expression can be multiplied by one without changing its value.
It is used to go from one unit to another.
How Does Dimensional Analysis Work?
A conversion factor, or a fraction that is equal to one, is used, along with what you’re given, to determine what the new unit will be.
Dimensional Analysis
What happens when you divide a number by itself?
What happens when you divide a unit by itself?
In both cases, you get the number 1.
Dimensional analysis involves multiplication and division.
“Canceling” out Words
inches feet
feet miles
seconds hours
minutes seconds
inches
miles
hours
minutes
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.
Examples of Conversions
You can write any conversion as a fraction.
Be careful how you write that fraction. For example, you can write
60 s = 1 min as 60s or 1 min 1 min 60 s
Conversion factors To convert between units: Figure out what CONVERSION
FACTOR you need to perform your calculation
There are 12 inches in 1 foot 12 inches or 1 foot
1 foot 12 inches
Let’s try some examples together…
1. Suppose there are 12 slices of pizza in one pizza. How many slices are in 7 pizzas?
Given: 7 pizzasWant: # of slices
Conversion: 12 slices = one pizza
7 pizzas1
Solution
Check your work…
X 12 slices1 pizza = 84 slices
Let’s try some examples together…
2. How old are you in days?
Given: 17 yearsWant: # of days
Conversion: 365 days = one year
Solution
Check your work…
17 years1
X 365 days1 year = 6052 days
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 yearsWant: # of days
Conversion #1: 365 days = one yearConversion #2: 24 hours = one day
Solution
Check your work…
17 years1
X365 days
1 year X24 hours
1 day =
148,920 hours
Fill in the Missing Numbers( conversion factors)
1 foot = _____ inches
1 meter = _____ centimeters
1 pound = _______ ounces
1 minute = ______ seconds
1 hour = ________ minutes
12
100
16
60
60
Practice: Choose the appropriate conversion factor.
Inches to feet 1 ft
12 in.12 in.
1 ft
Minutes to hours60 min
1 hr
1 hr
60 min
Meters to centimeters 1 m
100 cm
100 cm
1 m
inches
1
minutes
1
meters
1
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
First- learn the metric prefixes
› Kilo
So 1 km = 1000 m› Centi › So 100 cm = 1 m› Milli
So 1000 mm = 1m
Be able to use a chart for the others!