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Despite the title, we're not going to a parallel universe in this section. Instead, I'm going to talk about a useful technique called dimensional analysis.

Dimensional analysis can be used in a couple of different ways. The first way is to convert from one unit to another, say from meters per second (m/s) to miles per hour (mph). In that, it may seem boring, but can be pretty helpful. If you have a conversion table handy, you don't really need to use dimensional analysis to change from one unit to the next. But if your table doesn't have the unit you want, you can use dimensional analysis to help use your conversion table to do the work, instead of just having to give up.

The other major way in which dimensional analysis can be used is to check whether or not the units on an answer you get in a problem make sense. For example, if I tell you how far it is to Disneyland from the Price Center, and tell you how long it takes me to drive to Disneyland from the Price Center, I might ask you to tell me my average speed along the drive (but not to tell the CHP, of course). You probably know that the average speed is just the distance I drove, divided by the time it took me. So your answer should have units which are distance divided by time, like miles per hour. If you get hours per mile, you've got it backwards.

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Greg Anderson
Tue Jan 14 10:38:34 PST 1997