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Jump to one of the following dimensional analysis parts:   Choose One Introduction to Dimensional Analysis Part 1- The Need for Units Part 2- Setting up Conversions Part 3- Basic Conversion Problems Part 4- Complex Conversion Problems Part 5- Problem Dissection I Part 6- Problem Dissection II Part 7- Density Problems Part 8- Quizzes

Let's build off of the problem we left on in the previous section. Remember that you were to calculate the number of gallons you could get with $10.00 and gasoline at $1.45/gallon. Pressing the "cycle" button will cycle you through the setup, unit check, and the final calculation (this is the way many of the problems will work from now on in this section.

Here's the list of rules.

OK. What if you had wanted to know not how many gallons you could get, but how many miles you could drive assuming your car gets 44.2 miles a gallon? Let's try building from the previous problem.

But there's another way to do this problem. Instead of chopping it up into separate pieces, build it as one problem. Not all problems lend themselves to working them this way but many of them do. It's a nice, elegant way to minimize the number of calculations you have to do. Let's reintroduce the problem.

You have a ten dollar bill and you need to get gas for your car. If gas is $1.45 a gallon and your car gets 44.2 miles per gallon, how many miles will you be able to drive your car on ten dollars?

I refer to this as a complex problem not because it's difficult but because it involves more than one conversion. Which way do you have to do a complex problem of this sort? Whichever way works best for you. I will strongly suggest that you learn to do problems using the method of stringing together conversions instead of working them out one at a time. Once you feel comfortable with this method you find that you can solve problems somewhat faster than the single conversion method.

To illustrate my point, let's continue building off of the previous problem.

You have a ten dollar bill and you need to get gas for your car. Gas currently costs $1.45 a gallon and your car averages 44.2 miles a gallon. If you drive, on average, 10.1 miles a day, how many weeks will you be able to drive on a ten dollar fillup?

Wow! I wish I really could go that long on ten dollars! A comment on significant figures for this problem. The 7 days a week conversion is an exact one since there are exactly 7 days per week. There is no doubt involved. Additionally, using money in problems where you have to track significant figures is a little problematic. Dollar amounts are also exact. The final number of significant figures is due to both the gas milage and the measured number of driving miles per day since they both have 3 significant figures.

The next three sections will look at three different problems and help you learn how to analyze, set up, and work through more complex problems.