What is Dimensional Analysis?


A fancy term for converting from one unit to another
Examples …
Going from dollars to cents
Going from miles to kilometers
Going from meters to cm to inches
Going from seconds to years
Going from mph to m/s

What is Dimensional Analysis?


I will teach you a systematic way of doing these problems
The method uses conversion factors

Some Typical Conversion Factors
60 s = 1 min as 60 s or 1 min
1 min 60 s
1.6 km = 1 mile as 1.6 km or 1 mile
1 mile 1.6 km
13.38 US dollars = 0.075 Mexican pesos as 13.38 USD or 0.075 pesos
0.075 pesos 13.38 USD

How Does Dimensional
Analysis Work?
 A conversion factor is used, along with what you’re given, to determine what the new unit will be.
 Enough talk lets do one or two on the board!!!

Examples of Conversions


Again, just be careful how you write the fraction.
The fraction must be written so that like units cancel .

Steps
1.
2.
3.
4.
5.
Start with the given value.
Write the multiplication symbol.
Choose the appropriate conversion factor.
The problem is solved by multiplying the given data & their units by the appropriate unit factors so that the desired units remain.
Remember, cancel like units.

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 pizzas
Want: # of slices
Conversion: 12 slices = one pizza

Solution

Check your work…
7 pizzas
1
X
12 slices
1 pizza
=
84 slices

Let’s try some examples together…
2.
How old are you in days?
Given: 17 years
Want: # of days
Conversion: 365 days = one year

Solution

Check your work…
17 years
1
X
365 days
1 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 years
Want: # of days
Conversion #1: 365 days = one year
Conversion #2: 24 hours = one day

Solution

Check your work…
17 years
1
X
365 days
1 year
X
24 hours
1 day
=
148,920 hours