Before getting into those concepts though, I want to provide a quick tutorial for new students (or a refresher for others) on unit conversions, and then briefly discuss Dimensional Analysis. Understanding how to convert units can often point you to the correct way of solving problems. I previously posted on strategies that can be used for solving word problems, and also how to deal with unit conversions. I'll link to it from here, rather than going through it again. But please post comments and questions if there is anything more about it that you would like clarified.
Similar to unit conversions is Dimensional Analysis. What this is, is exactly what it sounds like... analyzing the dimensions of the problem. You need to make sure that the dimensions (units) of one side of the equation is equal to the dimensions (units) on the other. If they are not, you know you have done something wrong. Using a common example and knowing that velocity is equal to distance per unit time:
distance = velocity * time....
distance = (distance/time) * time....
distance = distance
Therefore, the dimensions of this equation make sense. You can similarly approach this by looking at the units, as described above and on the previous link.
meters = meters/sec * sec
meters = meters
The units make sense.
As you can see, Dimensional Analysis isn't as tricky as it sounds. You basically just check to make sure that the dimensions, or units, are the same on either side of the equals sign.
In my next posts, I would like to discuss Scientific Notation and Significant Figures... concepts that are notorious for giving students problems. I will try my best to clear things up. :)