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Most of the numbers you will be dealing with in your earth science course will be attached to units of measurement which describe some property of the earth. You must include the correct units of measurement in answers to math-based questions, or your answers are wrong. If, for example, you asked someone how long it would take to fix your car, and they answered "4," would that mean 4 minutes, 4 hours, 4 days or 4 months? Mathematical answers are essentially meaningless without the proper units of measurement.
From a practical standpoint, paying careful attention to cancelling units as you work a problem will increase the chance of arriving at the correct answer. In math courses this is called "dimensional analysis." Consider the following problem:
A large earthquake has ruptured the seafloor near Alaska and has triggered a tsunami (a seismic sea wave). The wave travels at a speed of 650 km/hr through the ocean. How much time does a coastal city located 2,000 km from the earthquake epicenter have to evacuate residents before the first wave arrives?
This is an example of a time, distance, rate problem. In this case you know the rate and distance, and need to calculate the time. Students may forget whether they need to multiply or divide to get the correct answer. This is where keeping track of units will tell you immediately if you've done the problem correctly.
First, multiply the numbers together and see what happens:
650 km/hr x 2,000 km = 1,300,000 km2/hr
Note that km2/hr are not units of time, and this answer makes no sense. Now try the following:
650 km/hr ÷ 2,000 km = 0.325/hr
Again, we've arrived at an answer that makes no sense. The kilometers have cancelled out in the case, but the hours have remained in the denominator (bottom) of the formula, and thus our answer is expressed in "per hours." Now try the third possible combination (the distance divided by the rate):
2,000 km ÷ 650 km/hr = 3.08 hr
Now we have an answer that makes sense, and as long as the computations have been done correctly we can be confident in our answer.
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06/25/0313 Oct 2009 09:18:40 -0700