Dosage Calculation Using the Dimensional Analysis Method

CHAPTER 16


Dosage Calculation Using the Dimensional Analysis Method



Objectives


After reviewing this chapter, you should be able to:


1. Define dimensional analysis


2. Implement unit cancellation in dimensional analysis


3. Perform conversions using dimensional analysis


4. Use dimensional analysis to calculate dosages


Dimensional analysis is the use of a simple technique with a fancy name for the process of manipulating units. By manipulating units you are able to eliminate or cancel unwanted units. It is considered to be a common-sense approach that eliminates the need to memorize a formula. Once the concepts related to dimensional analysis are mastered it can be used to calculate dosages.


Dimensional analysis is also referred to as the factor-label method or the unit factor method. Dimensional analysis can be viewed as a problem-solving method. The advantage of dimensional analysis is that because only one equation is needed, it eliminates memorization of formulas. Dimensional analysis can be used for all calculations you may encounter once you become comfortable with the process. This chapter will discuss dimensional analysis and provide examples of how it might be used in calculating dosages. Although some may find the formalism of the term dimensional analysis intimidating at first, you will find it is quite simple once you have worked a few problems. This method as stated can be used for all calculations. Dimensional analysis will be demonstrated as we proceed through the chapters. Note: Remember, as stated in the discussion of calculation methods, that it is important that you understand that you as the learner must choose a method of calculation you are comfortable with and use it consistently.



UNDERSTANDING THE BASICS OF DIMENSIONAL ANALYSIS


To introduce the basics relating to dimensional analysis, let’s begin by looking at how the process works in making conversions before we look at its use in calculating dosages. As you recall from previous chapters, you learned what were referred to as equivalents or conversion factors: for example, 1 g = 1,000 mg, 1 grain = 60 mg. When we begin using this process for dosage calculations, you will quickly see how dimensional analysis allows multiple factors to be entered in one equation. This method is particularly useful when you have a medication ordered in one unit and it is available in another unit. Although multiple factors can be placed in a dimensional analysis equation, you can decide to do the conversion before you set up the equation using one of the methods learned in earlier chapters, or you can use dimensional analysis to perform the conversion before calculating the dosage.



Performing Conversions Using Dimensional Analysis


The equivalents or conversion factors you learned can be written in a fraction format, which is important to understand in using dimensional analysis. Let’s look at the equivalent 1 kg = 1,000 g.


This can be written as:


1 kg1,000 g or 1,000 g1 kg


image

Now let’s look at the basics in using dimensional analysis for converting units of measure. It is necessary to state the equivalent (conversion factor) in fraction format, maintaining the desired unit in the numerator.



NOTE


You have not changed the value of the unit: you have simply rewritten the equivalency or conversion factor in a fraction format.



An equivalent (conversion factor) will give you two fractions:




To Make Conversions Using Dimensional Analysis







imageCritical Thinking


Stating the equivalent incorrectly will not allow you to eliminate desired units. Knowing when the equation is set up correctly is an important part of the concept of dimensional analysis.



Let’s look at examples to demonstrate the dimensional analysis process.





Example 2:

110 lb = ________ kg




RULE


Placing a 1 under a value does not alter the value of the number. What you desire or are looking for is labeled x.


Setup:


image


RULE


All factors entered in the equation must always include the quantity and unit of measure. State all answers following the rules of the system. When there is more than one equivalent for a unit of measure, use the conversion factor used most often.



image Practice Problems


Set up the following problems using the dimensional analysis format; cancel the units. Do not solve.




Answers on p. 622



Points to Remember





DOSAGE CALCULATION USING DIMENSIONAL ANALYSIS


As stated previously, dimensional analysis can be used to calculate dosages with the use of a single equation. A single equation can also be used to calculate the dosage when the dosage desired is in units that differ from what is available. When using dimensional analysis to calculate dosages, it is important to extract the essential information needed from the problem.


In earlier chapters relating to calculating dosages, you learned how to read medication labels. Remember, dosages are always expressed in relation to the form or unit of measure (e.g., milliliters) that contains them.


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Feb 11, 2017 | Posted by in PHARMACY | Comments Off on Dosage Calculation Using the Dimensional Analysis Method

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