Dimensional Analysis

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 DIVIDE!!!! 3 cm/50km =1 $1/1535.10 LBP=1

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 • 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) • Start with the given value and turn it into a fraction(put it over one) • Write the multiplication symbol. • 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… • 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

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

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… 6052 days 17 years 1 365 days 1 year X =

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… 6.81 inches 17.3 cm 1 1 inch 2.54 cm X = Be careful!!! The fraction bar means divide.

Now, you try… • Determine the number of eggs in 23 dozen eggs. • 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 years W: # of days R #1: 365 days = one year R #2: 24 hours = one day

Solution • Check your work… 17 years 1 365 days 1 year 24 hours 1 day X X = 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/h W: # m/s R #1: 1000 m = 1 km R #2: 1 hour = 60 minutes R #3: 1 minute = 60 seconds

Solution • Check your work… 83 m 1 hour 0.083 km 1 hour 1000 m 1 km X = 83 m 1 hour 1 hour 60 min 1 min 60 sec = X X 0.023 m sec

Solution • Check your work… 1 min 60 sec 0.083 km 1 hour 1 hour 60 min 1000 m 1 km X X X 0.023 m sec =

Dimensional Analysis