Unit conversion problems

Unit Conversion problems can appear to be more complicated than this one. However, they are not. They just involve more simple steps. 

You can work all unit conversion problems by this procedure. In some cases, such as the miles to feet problem, only one step is necessary. In other cases, such as the miles to inches problem, more than one step is necessary. However, all steps are of the same type. You will cancel one unit and get a new unit. This process continues until the new unit matches the one that you are seeking. 

Figure 4. The display that GEORGE uses to show the solution to a unit conversion problem. (Reproduced with permission from Ref. 3. Copyright 1985 COMPress.)...

The dimensional-analysis method and the use of ballpark checks are techniques that will help you solve problems of many kinds, not just unit conversions. Problems sometimes seem complicated, but you can usually sort out the complications by analyzing the problem properly ... 

The main purpose of this chapter is to show you how to make many different types of unit conversions, such as the one required above. You will find that the stepwise thought process associated with the procedure called unit analysis not only guides you in figuring out how to set up unit conversion problems but also gives you confidence that your answers are correct. 

You have seen some of the many uses of unit analysis and looked at various kinds of information that provide useful conversion factors for chemical calculations. Now, it is time for you to practice a general procedure for navigating your way through unit conversion problems so that you will be able to do them efficiently on your own. Sample Study Sheet 8.3 describes a stepwise thought process that can help you to decide what conversion factors to use and how to assemble them into a unit analysis format. 

Work on as many of the problems at the end of the chapter as you can. They review and extend the concepts and skills in the text. Answers are given in the back of the book for problems with a colored number, but try to solve them yourself first. Let s apply this approach in a unit-conversion problem. 

There are usually alternative sequences in unit-conversion problems. Here, for example, we would get the same answer if we first converted the cost of wire from /ft to /cm and kept the wire length in cm. Try it yourself. 

This is a unit conversion problem. You should come up with the following strategy to solve the problem. 

This is a somewhat elaborate unit conversion problem. We have to determine the number of SO2 molecules present in a ton—so the molar mass would have to be calculated after looking up the appropriate molar masses for sulfor and oxygen. Then, convert tons to pounds, pounds to grams, grams to moles, and moles to molecules (using Avogadro s number). This number would be the number of molecules per 300 so we d have to divide by 300 to get the number of molecules per dollar. 

In Examples 2.8 and 2.9, you will find this problem-solving procedure applied to unit conversion problems. The procedure is summarized in the left column, and two examples of applying the procedure are shown in the middle and right columns. This three-column format is used in selected examples throughout this text. It allows you to see how a particular procedure can be applied to two different problems. Work through one problem first (from top to bottom) and then examine how the same procedure is applied to the other problem. Recognizing the commonalities and differences between problems is a key part of problem solving. 

EXAMPLE 2.10 Solving MuKistep Unit Conversion Problems... 

In this chapter, you have seen a few examples of how to solve numerical problems. In Section 2.6, we developed a procedure to solve simple unit conversion problems. We then learned how to modify that procedure to work with multistep unit conversion problems and problems involving an equation. We will now sirni-marize and generalize these procedures and apply them to two additional examples. As we did in Section 2.6, we provide the general procedure for solving nmnerical problems in the left colmnn and the application of the procedure to two examples in the center and right columns. 

Solve unit conversion problems by following these steps. 

Solve unit conversion problems using the problemsolving strategies outlined in Section 2.6. 

This is a unit conversion problem. To convert to the appropriate units, use the con-vCTsion factors presented in Table 5.2 and the techniques presented in Chapter 1. Keep in mind that the conversion 760 mmHg = 1 atm is exact. 

It is important to remember to follow the rules of significant figures in these unit conversion problems. Notice in this case that there are exactly three feet per yard (infinite number of significant figures—rule 5 in Table 2.1). Thus the answer to the calculation should have the same number of significant figures as in the number 15, which is two. The correct answer is therefore 5.0 yards, not 5 yards. 

Most unit conversion problems take the following form ... 

Strategize. This is usually the most challenging part of solving a problem. In this process, you must develop a conceptual plan—a series of steps that will get you from the given information to the information you are trying to find. You have already seen conceptual plans for simple unit conversion problems. Each arrow in a conceptual plan represents a computational step. On the left side of the arrow is the quantity you had before the step, on the right side of the arrow is the quantity you will have after the step, and below the arrow is the information you need to get from one to the other—the relationship between the quantities. 

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