dimensional analysis

Dimensional Analysis

Homework

Objectives

• Be able to convert between units using dimensional analysis

Dimensional Analysis

• A VERY helpful skill in science, and one that will get especially helpful in chemistry and physics… Dimensional Analysis It will also be another way of converting

prefixes that some of you may prefer to hopping the decimal place

• This will take PRACTICE to master

Dimensional Analysis

• Dimensional analysis is a method of converting a measurement from one unit to another

• Example: How many seconds is 2 hours?

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Dimensional Analysis

• First and most important in any dimensional analysis problem 1. Identify the unit your measurement is

already in, and identify the unit you want your measurement to end up in.

• Example: Measurement is already in hours. We want it in seconds.

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Dimensional Analysis

• 2. If you don’t know how many of your starting unit directly equals your ending unit, make a chain. I don’t know off the top of my head how many seconds

are in an hour, for instance. But I know how many seconds are in a minute, and how many minutes are in an hour. Ex: Hours -> Minutes -> Seconds will be my chain.

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Dimensional Analysis

3. Begin your chain with your starting measurement Write it as a fraction with a denominator of 1. Ex: 2 hrs 1

NOTE: IT IS SUPER SUPER IMPORTANT WHEN DOING THESE PROBLEMS TO ALWAYS WRITE YOUR UNITS.

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Dimensional Analysis

• 4. The next fraction in your chain will be an “equivalence.” The top of the fraction equals the bottom. Ex: It will be 60 min or 1 hr

1 hr 60 min

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Dimensional Analysis

• 5. Write the fraction so that it will “criss-cross”: the bottom will have the same unit as the previous fraction’s top did. Ex: We will choose 60 min

1 hr

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Dimensional Analysis

• 6. Repeat steps 4-5 until you reach an equivalence that includes your ending unit. Ex: The next and last equivalence will be 60 sec

1 min

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Dimensional Analysis

• Choose the step seven that you prefer. EITHER:

• 7. Your answer will be this division: (All the top numbers multiplied together)/(All the bottom numbers multiplied together) and your final unit. Ex: (2 x 60 x 60)/(1 x 1 x 1) sec = 7200 sec

OR• 7. Do each division one at a time, and multiply them as

you go along. Ex: (2/1) x (60/1) x (60/1) sec = 2 x 60 x 60 sec = 7200 sec

Dimensional Analysis

• 8. Round your final answer to the same number of sig figs as your starting measurement. Ex: 2 hours has 1 sig fig. 7200 seconds -> 7000

seconds.

Dimensional Analysis

• Another, shorter example:

• How many seconds are in five minutes? Before we write it out: What are our starting and finishing unit? What equivalences will we need?

Dimensional Analysis

• A little harder:

• How many minutes is 47 seconds?

Dimensional Analysis

• And harder:

• How many seconds is 1.89 days?

Dimensional Analysis

• Use the equivalences given on the handout to do this one with me:

• How many feet are in 2 meters?

Dimensional Analysis

• How many meters are in 850 inches?

Dimensional Analysis

• Whiteboard Practice

Dimensional Analysis

Homework

Objectives

• Practice Dimensional Analysis

Practice Quiz

• With your partner, write ten dimensional analysis problems for another team. One partner, write the quiz paper. Other partner, write the answer key

INCLUDING ALL WORK. In order to get a problem correct, they must

show all work with units by every number, and have their answer in the correct sig figs.