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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

Perhaps the most difficult aspect of solving problems is trying to figure out just what's being asked. How many times have you sat stumped over a homework problem while you spin your wheels just trying to wade through the problem to no avail? Hopefully, the rules given previously will help you at least a little. The next three sections will look at three more complicated problems and break them down. The thought process is very important. The less time you spend figuring out a problem means more time working on solving it. So, let's solve one.

Which of the following is the longest length?

1. 3.005 x 10³ decimeters
2. 1.522 x 10^-3 megameters
3. 6.563 x 10⁴ inches
4. 3.122 x 10⁸ micrometers
5. 3.242 x 10² feet

Seems to be a fairly straight-forward problem. If you had been asked to compare a number of currency amounts, you could probably whip through it pretty quickly because you've been converting between different monetary values all your life. Pennies to nickels to dimes to quarters to dollars to five dollars to ten dollars and on and on. If you wanted to know which was greater, 460 pennies or 4 dollar bills, you'd probably convert the pennies into 4 dollars and 60 sixty cents. Thus, the 460 pennies would win.

You do something very similar in a problem like this one. Convert all the lengths into a common unit of length and then compare them. Additionally, I'd keep everything in scientific notation to eliminate any decimal place confusion between similar values. What we've really got is a total of 6 problems. 5 of the problems involve converting the units. The 6^th question is the key since what's being asked is to choose which one is the greatest length.

Here's the list of rules.

Here's a basic list of unit conversions.

Let's attack each of the 5 lengths and convert them into a common unit. I'll use meters since it's convenient due to 3 of them already being in metric units. Just like previous, you can cycle through each of the conversions in turn to see not only the answer but to see how the units work out.

1: 3.005 x 10³ decimeters.

2: 1.522 x 10^-3 megameters.

3: 6.563 x 10⁴ inches.

4: 3.122 x 10⁸ micrometers.

5: 3.242 x 10² feet.

Now all we have to do is tabulate the data and compare the lengths-

The greatest length is choice 3, 6.563 x 10⁴ inches.