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Dimensional Analysis Tutorial

Part 1: The Need For Units

In your algebra and similar math classes, you're used to working with numbers and formulas. In fact, it's likely to be second nature to many of you. The trick is to now apply all that hard work in those math classes to solving problems in your other classes. You have the tools but you need to be able to apply them when appropriate. A difficult concept for some people is that numbers are now useless without their corresponding units (for the most part). It's not enough to just put the units in at the end because if you do that, you are assuming that you did the problem correctly. You'll learn as you work throught this tutorial that units will be your first verification check.

Here's a few situations for you to think about-

You go to the store with a friend and she asks you for 50. Is that 50 cents or 50 dollars? I think your wallet will agree with me when I suggest there's a big difference between the two.
At a baseball game you get distracted only to have someone next to you comment on how that ball just got hit 500. 500 feet and if it's fair, it's a homerun. 500 inches doesn't even get it out of the infield and unless it's a sacrifice or a bunt, it's a bit of a bummer for the team at bat.
Your wife tells you to make sure you get one something of diapers when you go to the store. Is that one mega, jumbo, or regular package of diapers? I guarantee that if you come home with only one diaper you'll be sleeping on the couch for quite a few days!
You're driving on the freeway and you get stopped by a police officer who proceeds to state that you were traveling approximately 105. Now if that's in miles/hour then you've got an expensive speeding ticket regardless of where you're driving in the USA. However, if that's in kilometers/hour then it's the equivalent of about 65 miles/hour which is, hopefully, the posted limit. In that case, the officer is probably just thanking you for obeying the law.

You can either jump into the idea of dimensional analysis with enthusiasm or be dragged kicking-and-screaming. In my class, I will take points off of calculations without units whether you have a correct answer or not. Whichever one works for you... I hope that after this tutorial you will see just how useful this concept happens to be.

Something else to get used to is the idea that units will be treated just like numbers. Units will be multiplied and divided and if the units don't cancel out to what's needed, you'll know that you've worked the problem incorrectly. This is not something that is natural to most people. You have to work homework problems the same way you work exam questions. If you don't do it before the exam, why should you expect to be able to suddenly do it during the exam? Practice doesn't make perfect; but; proper practice is a different ballgame, though! You'll discover just how much easier it is once you've practiced a lot, also.