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 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 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 = LBP 3 cm/50km =1 $1/ 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 write 60 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 pizzas Wanted: # of slices Conversion/Relationship: 12 slices = one pizza

7 pizzas 1 Solution Check your work…did you end up with the correct units? X 12 slices 1 pizza = 84 slices

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

Solution Check your work… 17 years 1 X 365 days 1 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 cm W: # of inches R: 2.54 cm = one inch

Solution Check your work… 17.3 cm 1 X 1 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 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 years W: # of days R #1: 365 days = one year R #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

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 km/h into m/s. G: km/h W: # m/s R #1: 1000 m = 1 km R #2: 1 hour = 60 minutes R #3: 1 minute = 60 seconds

83 m 1 hour Solution Check your work… km 1 hour X 1000 m 1 km X 1 hour 60 min = m sec 83 m 1 hour X 1 min 60 sec =

Solution Check your work… km 1 hour X 1000 m 1 km X 1 hour 60 min m sec X 1 min 60 sec =