Date post: | 13-Jan-2016 |
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Dimensional Analysis
What is Dimensional Analysis?
Let’s think about a map… Map-small scale representation of a
large area How is that helpful? Thankfully, we can convert from small-
scale units to large-scale and use the information in real life.
How? DA
What is Dimensional Analysis?
Ex: 3 cm = 50 km
What is Dimensional Analysis?
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.
How do we do this??? DA
What is Dimensional Analysis?
Whenever you use a map or 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 is a fraction that is equal to one
It is used, along with what you’re given, to determine what the new unit will be.
How Does Dimensional Analysis Work?
In our previous discussions, you could say that 3 cm equals 50 km on the map or that $1 equals 1535.10 Lebanese Pounds (LBP).
How Does Dimensional Analysis Work?
If we write these expressions mathematically, they would look like
How can you make them equal to one?
3 cm = 50 km$1 = 1535.10 LBP
3 cm/50km =1$1/1535.10 LBP=1
DIVIDE!!!!
Examples of Conversions
You can write any conversion as a fraction.
Every conversion can be written as two different fractions.
For example, you can write60 s = 1 min
60s or 1 min 1 min 60 s
Examples of Conversions
The fraction must be written so that like units cancel.
Steps a. If you have a word problem, identify the
given information (g), the wanted information (w) and the conversions or relationships needed (r) (If you don’t have a word problem start with number 2)
b. Start with the given value and turn it into a fraction (put it over one)
c. Write the multiplication symbol.d. Multiply the given data by the appropriate
conversion factors so that like units cancel and the desired units remain.
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 pizzasWanted: # of slices
Conversion/Relationship: 12 slices = one pizza
7 pizzas1
Solution
Check your work…did you end up with the correct units?
X12 slices1 pizza = 84 slices
Let’s try some examples together…
2. How old are you in days?
Given: 17 yearsWanted: # of days
Conversion/Relationship:365 days = one year
Solution
Check your work…
17 years1
X 365 days1 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?
G: 17.3 cmW: # of inches
R: 2.54 cm = one inch
Solution
Check your work…
17.3 cm1
X1 inch
2.54 cm = 6.81 inches
Be careful!!! The fraction bar means divide.
Now, you try…
1. Determine the number of eggs in 23 dozen eggs.
2. If one package of gum has 10 pieces, how many pieces are in 0.023 packages of gum?
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?
G: 17 yearsW: # of days
R #1: 365 days = one yearR #2: 24 hours = one day
Solution
Check your work…
17 years1
X365 days
1 year X24 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.
G: 0.083 km/hW: # m/s
R #1: 1000 m = 1 kmR #2: 1 hour = 60 minutes
R #3: 1 minute = 60 seconds
83 m1 hour
Solution
Check your work…
0.083 km1 hour
X 1000 m1 km
X1 hour60 min
=
0.023 msec
83 m1 hour
X1 min60 sec
=
Solution
Check your work…
0.083 km1 hour
X 1000 m1 km
X1 hour60 min
0.023 msec
X1 min60 sec
=