Dimensional analysis (also known as the factor-label method or unit-factor method or UNIT ANALYSIS) is by far the most useful math trick you’ll ever learn. Maybe you’ve learned some algebra, but will you use it? For many people the answer is, “not after the final exam.”

For a fraction of the effort needed to learn algebra, you too can learn “dimensional analysis.” First off, however, let’s get rid of the big words. What this is all about is just conversion—converting one thing to another. This is something you will have occasion to do in real life. This is seriously useful stuff.

This trick is about applied math, not about numbers in the abstract. We’re talking about measurable stuff, stuff you can count. Anything you measure will have a number with some sort of “unit of measure” (the dimension) attached. A unit could be miles, gallons, miles per second, peas per pod, or pizza slices per person.

Source: Fun with Dimensional Analysis

Two Sample Problems (see web site for more):

• Rate Problems: If you are going 50 miles per hour, how many feet per second are you traveling?
  (Sometimes you need to convert both numerator and denominator)…
• Mixing Problems: How much bleach would you need to make a quart of 5 percent bleach solution? Continue reading →