⏳ Estimated Reading/Watching Time: 8 - 10 minutes

In this lesson, you will learn how to convert between different units using dimensional analysis.

Dimensional Analysis

Dimensional analysis is a way to convert a quantity given in one unit to an equal quantity of another unit by lining up all the known values and multiplying. It is sometimes called factor-labeling or simply doing "conversions".

The best way to start a dimensional analysis problem is by using what you already know. In some cases, you may use more steps than a classmate to find the same answer, but it doesn't matter. Use what you know, even if the problem goes all the way across the page!

In a dimensional analysis problem, start with your given value and unit and then work toward your desired unit by writing equal values side by side. Remember you want to cancel each of the intermediate units. To cancel a unit on the top part of the problem, you have to get the unit on the bottom. Likewise, to cancel a unit that appears on the bottom part of the problem, you have to write it in on the top.

Once you have the problem written out, multiply across the top and bottom and then divide the top by the bottom.

In lots of APES problems, you will need to convert both the top and bottom units. Don't panic! Just convert the top one first and then the bottom one.

Watch the short video below to learn how to do complex conversion problems:

AP Exam Tip

You WILL have to show your work for dimensional analysis problems on the free response portion of the AP exam to earn credit.

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