Lesson 2

A Simple Example

You've done conversion factor calculations before you even came to a chemistry class. For example, how many inches are there in two feet? The answer, or course, is 24 inches. I'm sure you could figure that out quickly, almost without thinking about it, simply because you have dealt with that kind of question before.

But now, I'd like you to think about it, not just do it automatically. How is it you came up with 24 inches from 2 feet? Well, you multiply 2 by 12. That gives you 24. But why multiply by 12? You multiply by 12 because there are 12 inches in one foot. This is set up in a rather formal fashion here (and in example 13 in your workbook). Let's go through the process step by step.

This is what we call the conversion factor method. It also goes by other names. We start with "2 feet." We are going to change this to "inches," that is find out what 2 feet is equal to in inches. To do this we can multiply by a conversion factor that will change from feet (that goes on the bottom) to inches (that goes on the top). The equivalence between feet and inches goes into the conversion factor. The top part (the numerator) of the conversion factor has to be equivalent to the bottom part (the denominator). The relationship, of course, is that 12 inches is the same as 1 foot. Because the unit "foot" is in the denominator, it will cancel with the feet that we started with, leaving us with the unit "inches." Then calculating 2 x 12 ÷ 1 tells us that we have 24 inches.

This has been a somewhat ridiculous example. To work out this problem in this way makes a difficult problem out of a simple one. If you can work out a problem simply, do so. The purpose of the example is to use something very familiar to introduce what may be a new technique.

Another Simple Example

Let's go through another similar example. How many feet are there in 30 inches? (This is also shown in example 14 in your workbook).

Here we want to change inches into feet. So, let's find out how many feet there are in 30 inches. Write down 30 inches first and then the conversion factor with inches on the bottom and feet on the top. The reason for this is that we are changing from inches to feet. then put the right numbers with the units. So we have to multiply by 1 foot over 12 inches to get the correct answer. The inches cancel out, and 30 times 1 divided by 12 gives 2.5 feet as the final answer.

Purpose of These Examples

The purpose of these examples has been to show you a method for doing certain types of calculations, even though you might be able to solve these particular examples without using the method.

In these examples a measurement made in one unit (such as feet) was converted into another unit (such as inches). To work these kinds of problems, you need to have a conversion factor--a relationship between the units. In these examples you needed to know that one foot equals 12 inches.