Dimensional Analysis Conversions Objectives n SWBAT convert between

Dimensional Analysis Conversions!

Objectives n SWBAT convert between different units in the metric system.

What is Dimensional Analysis? n n Have you ever used a map? Since the map is a small-scale representation of a large area, there is a scale that you can use to convert from small-scale units to large-scale units—for example, going from inches to miles or from cm to km.

What is Dimensional Analysis? Ex: 3 cm = 50 km

What is Dimensional Analysis? n n n 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? n Dimensional Analysis: Converting from one unit to another.

How Does Dimensional Analysis Work? n A conversion factor, or a fraction that is used to go from one unit of measurement to another

Examples of Conversions n n n You can write any conversion as a fraction. Be careful how you write the fraction. For example, you can write 60 s = 1 min as 60 s or 1 min 60 s

Examples of Conversions n The fraction must be written so that like units cancel.

Steps to Convert 1. 2. 3. 4. 5. 6. Write the GIVEN Write the multiplication symbol. Draw a division Line Put the GIVEN units on the bottom of the division line Put the Units you want on the top of the division line Write the conversion numbers next to the correct units

Example 1: 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 n Check your work… 7 pizzas 1 X 12 slices 1 pizza = 84 slices

Example 2 2. How old are you in days? Convert from years Given: 15 years Want: # of days Conversion: 365 days = one year

Solution n Check your work… 15 years 1 X 365 days 1 year = 5475 days

Example 3: 3. There are 2. 54 cm in one inch. How many inches are in 17. 3 cm? Given: 17. 3 cm Want: # of inches Conversion: 2. 54 cm = one inch

Solution n Check your work… 17. 3 cm 1 X 1 inch 2. 54 cm = Be careful!!! The fraction bar means divide. 6. 81 inches

Practice: 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 Conversions Problems n n Sometimes, you will need to use multiple conversion factors to solve a problem. Go slow and check that all of your units cancel except for your final units. Remember: new units go on top!

Example 1 n The oldest person to ever live died at the age of 122 years old. How many hours old was she?

Example 2 n Most classes here at Northtown are 1 hour long. How many seconds long is each class?

Example 3 n Mr. Willert drove 718, 900 inches to a nearby grocery store. How many miles did he travel?

Practice 1 n Ms. Duran flew 1, 744 miles home to Los Angeles for winter break. How many inches did she fly?