Chapter 5 • Convert among metric, household, and apothecary systems using ratio and proportion • Convert among metric, household, and apothecary systems using dimensional analysis When making conversions between two measurement systems, the answers will usually not be exact, and the accepted difference between the measurement systems is in the range of 10% either above or below the actual calculated amount. Other factors in calculating approximate measurements do exist, such as the viscosity of the medication and the size of the utensils that will be used to provide the medication. In this text, please be sure that your conversion is as close to an exact amount as possible, so use the conversion factor that will give you an answer that can be administered with the utensil available. For example, in some cases a teaspoon may be 4 milliliters, but in others, when calculating a teaspoon, the conversion may be 5 milliliters. In these cases, you will need to complete the problem using both conversions to find the answer that is measurable. You always want to find the measurable amount for the ease of administration. For example, if your answer from the conversion indicates 4.4 milliliters is to be administered and this medication will be given with a utensil holding either 4 or 5 milliliters, such as a dosespoon, you would indicate that 4 milliliters would be given; however, if this is being given with a teaspoon that holds 5 milliliters, measuring 4.4 milliliters would not be possible, so you would state to administer a teaspoon of medication. Finally, if the dosespoon or other measurement utensil is found in 0.01-milliliter increments, the exact amount may be administered. This concept is difficult to understand, but as you go through this chapter, please use the conversion factor that supplies the approximate dose that is measurable. Also remember that some of the conversions used in the mathematical calculations in this chapter are based on the materials presented in Chapter 4. This text builds on previously learned materials, and materials in previous chapters will be important for use starting with this chapter on conversions among measurement systems. In the previous chapter you learned the basic measurements found in the household, metric, and apothecary systems of measurements. Each of these is used today in prescribing and administering medications. Another measurement system, avoirdupois, is also available, but this system is not normally found in calculations or conversions. In this system, 16 ounces = one pound (7000 grains = one pound). Two other measures are used in dosage calculations—milliequivalents and units—that will be discussed in Chapter 6. Conversions among the systems are only necessary if the two factors needed for calculation are not found within the same measurement system. If both factors are already in the metric system, then moving within the system is all that is necessary, as seen in Chapter 4. This is likewise true for the apothecary and household measurements. However, if one factor is in one system, such as the metric system, and the other factor is in another system, such as household, proportional equations are used to find the unknown approximation. Ratio is the relationship of one quantity to another, whereas proportion is the relationship between two equal ratios. In ratio and proportion, an unknown is solved using “x” as the unknown. This provides a logical and systematic means of finding the equivalent unknown when knowns are used for calculations. Two equal ratio sets (or the relationship between two equivalents, such as a [extreme] : b [mean] :: c [mean] : d [extreme]) is indicated for calculating proportional equivalents. When one of the equivalents is unknown, an “x” is used to indicate the unknown. (See Chapter 2 if you need to review this material.) When the ratios have been properly aligned into proportion(s), multiply the two inside numbers (means, or “insies”) and the two outside numbers (extremes, or “outsies”) and then solve for “x.” Remember that what is done to numbers on one side of the equation must be done to numbers on the other side of the equation. If you need more review for ratio and proportion, refer to Chapter 2. 1. Find the known, or given, quantity— 2. What is the desired, or wanted, amount?—x tablespoons. 3. What are the conversion factors that are needed to make the necessary calculation? In this case, we need to know that 2 tablespoons equals 1 oz and 8 oz equals 1 c. 4. Set up the problem with factors that are available for conversion factors. You want to cancel out like factors by placing them in a numerator of the first fraction followed by the denominator in the next fraction as follows: 5. Cross out the unwanted units. Just as with any other mathematical equation, if units appear in both the numerator and the denominator, you may cancel them to find the unit that is desired. In this case, the remaining unit is a tablespoon, which is the unit you are seeking. 6. Multiply the numerators, multiply the denominators, and divide the product of the numerators by the product of the denominators. This will give you the desired quantity that was originally your unknown factor. So, after completing the problem: Now let’s look at other examples found within the same measurement systems. The apothecary system has only a few significant measurements that, although not commonly used, do convert into household measurements. Of importance are minims to drops, drams to teaspoons, and ounces to tablespoons (Figure 5-1). Cups, pints, quarts, and gallons are used by both systems. Length is not found in the apothecary system, so the conversions are not included in Table 5-1. As the chapter unfolds, the metric system will be added to combined tables for conversions among measurement systems. TABLE 5.1 Conversions between Apothecary and Household Systems of Measurement *Note that an apothecary pound contains only 12 oz, while a household pound contains 16 oz.
Conversions among Measurement Systems
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Introduction
Using Ratio and Proportion for Conversion of Units
Using Dimensional Analysis for Converting Among Units
c.
Conversions Between Household and Apothecary Systems
PARAMETER
APOTHECARY UNITS
HOUSEHOLD UNITS
METRIC UNITS
Volume
i (1 minim)
1 gtt (1 drop)
—
i (1 dram, 
60)
1 tsp (1 teaspoon)
—
(
ounce)
1 tbsp (1 tablespoon, 3 tsp)
—
i (1 oz)
2 tbsp (2 tbsp, 6 tsp)
—
viii
1 c (8 oz, 1 cup, 
pint)
—
1 pt (1 pint, 2 c, 
xvi)
1 pt (1 pint, 2 c, 16 oz)
—
1 qt (1 quart, 2 pt, 4 c, 
32)
1 qt (1 quart, 2 pt, 4 c, 32 oz)
—
1 gal (4 qt, 8 pt, 16 c, 
128)
1 gal (4 qt, 8 pt, 16 c, 128 oz)
—
Mass/Weight
i (1 oz, 60 gr)*
1 oz
—
1# (1 lb, 
xii)
1# or 1 lb (16 oz)*
—
Length
N/A
N/A
—
__________
xxxii = __________ mL
vi = __________ gtts
= __________ mg
viii = __________ mL
__________
__________
__________
__________
__________
= __________ mg
= __________ mg
= __________ mg
vi = __________ tsp
xv = __________ tbsp
= __________ mg
vi = __________ tbsp
= __________ tsp
cup of an ingredient for a cake. At the time of baking, the only available measurement device is a tablespoon. How can you help the person baking the cake know the proper amount of the ingredient to be used when only a tablespoon is available? (
c = __________ tbsp)
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(dram) and 
(ounce).
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