Introduction

Three measurement systems are presently used in the medical field to calculate drug amounts in weight, length, or volume, although length is not as commonly used in the pharmaceutical field as in other medical disciplines. One of the three systems is used in the United States on a daily basis—the household measurement, or U.S. Customary system. This system uses measurements such as cups, teaspoons, and pints. The International System of Units (abbreviated SI from the French, Système International d’Unités), or the metric system, is used in most of the remaining world. Its measurements are milligrams, grams, milliliters, and so on. The apothecary system, which uses grains and drams, is an older system that has been used in pharmacy for many years but is used less frequently today. Knowledge of these three systems is absolutely necessary so you can interpret medication orders or prescriptions and to advise patients in administration of drugs as needed. To administer the correct amount of the medication on a consistent basis, the pharmacy technician must understand how to use the medication that was probably written on an order, whether a prescription or chart, in the metric, U.S. Customary, or apothecary system. The conversion of values from one system to another is discussed in the next chapter, but this chapter is designed to ensure that you have basic knowledge of the measurements, their abbreviations, and the system in which each occurs.

All three systems—household, metric, and apothecary—have units of measure for weight and volume. In the household system, weight is in pounds and ounces with volume in quarts, pints, cups, teaspoons, tablespoons, and the like. The metric system is based on grams for weight and liters for volume. Length is found in the household as yards, feet, and inches and in metric systems as meters. But length is not found in the apothecary system. The apothecary units of interest are grains for weight with drams and ounces for liquids.

Metric weight is the measurement used most often in pharmacy to show a dosage unit. Most medications are ordered and supplied by the weight of a drug in solid, liquid, or gaseous amounts such as milligrams or grains per tablet or per liquid amount such as milliliters. Household units of weights are usually seen in conversions for individual dosing at home and are found by volume rather than actual weight. We do not use pounds and ounces in dosage administration. Start thinking about metric units of weight—milligrams and grams—and remember that these weight measurements are most often used in the medical field because of accuracy and ease of the system based on units of 10. Other weight measurements include pounds and ounces in household weights, kilograms and micrograms in the metric system, and grains for the apothecary system.

Volume is capacity or how much a container of liquid medication holds. Amounts of medications per teaspoon or tablespoon would be the weight of medication found in the liquid measurement or dosage per volume. Volume measurements include milliliters, liters, quarts, pints, teaspoons, tablespoons, and minims or drops.

Length is used in household and metric systems to measure height or body circumference as well as length of a suture line. In pharmacy, length is only used to measure medications that require application to the body that must be measured in inches or centimeters or millimeters. In this case, the means of application is usually premarked on a dispensing paper for ease in ensuring that the correct amount of medication is being administered, such as with nitroglycerin ointment. Another pharmaceutical use of length is in finding body surface area (BSA) in which height and weight are compared for dosage calculation (BSA is discussed in Chapter 10). Length measurements also include inches, feet, centimeters, meters, kilometers, yards, and miles.

Some of the previously mentioned measurements are those you use daily, whereas others may be foreign and need explanation. This chapter covers the basic measurements per system, which are essential for learning conversions in Chapter 5.

Household Or U.S. Customary System

The household or U.S. customary system of measure is being introduced first because much of it is already familiar. From elementary school to the present, these measurements have been taught and used in your daily life, such as with cooking. Measurements are based on the English system of measures, which had its beginnings with the Greeks and Romans. These measurements will most likely be used in the home setting for administration of medications, although use of a measurement device that is provided with the medication increases patient safety. Therefore, you must be familiar with this system, although it is the least accurate of the measurement systems. In a hospital setting, these measurements would not be as appropriate.

Household measurements are expressed in Arabic numbers with the abbreviation for each following the number, such as 5 tsp or  pt. Table 4-1 provides the basic household measurements for weight accompanied by abbreviations and equivalents as appropriate.

Some medication labels include household measurements as well as metric measurements as seen on the label for Retrovir (Figure 4-1).

Table 4-2 gives the measurements of length often seen in the medical setting. A mile is also a measurement of length but is not used in pharmaceutical calculations.

Table 4-3 shows the household measurements of volume or liquid used most frequently in the home and in pharmaceutical calculations. Always remember that the size of a drop is totally dependent on the size of the opening in the dropper and viscosity of the liquid; therefore the 60 drops per teaspoon often found in measurement tables for household measurements is only an approximation. Drops used with intravenous therapy are stated in invariable amounts in the metric system as will be seen in later chapters. Also, household utensils are not necessarily accurate, so the amounts measured in these utensils should be considered only approximations.

Using Ratio and Proportion for Finding Equivalency with Household System

Points To Remember

Steps For Solving The Unknown Using Proportion

1. Identify the unknown unit of measurement.

2. Find the known equivalent for the problem to be solved.

3. Write the known equivalent on the left side of the proportion.

4. Write the unknown desired on the right side of the proportion with the identical measurements in the same positions in the equation (i.e., inches : feet :: inches : feet; tsp : tbsp :: tsp : tbsp; inches : feet :: inches : feet).

5. Solve the equation by cross-multiplication of means and extremes or use “insies” and “outsies.”

Example 4-1

4 ft = x inches

A known factor is 1 ft = 12 inches. Use ratio and proportion to calculate the number of inches in 4 feet.

Known Unknown

After cross multiplying the equation will be as follows:

1x=48 in

NOTE: ft may be cancelled because both equivalents of the same measurement are known and appear on both sides of the fractional equation.

So,4 ft=48inches because the“x”is asking for inches.

Example 4-2

In this example the known factor is 3 tsp = 1 tbsp. Using ratio and proportion the fractional equation is as follows:

4tbsp=_____tsp

Known Unknown

3tsp:1tbsp::xtsp:4tbsp

1x=12 tsp

NOTE: tbsp may be cancelled because both equivalents of the same measurement are known and appear on both sides of the fractional equation.

 Tech Alert

When calculating using ratio and proportion, be careful to place the designated measurement in the same position in each ratio. Place the known equivalents on the left side of the equation with the unknown on the right side of the equation. This will assist in being sure placement of the measurements is the same in each ratio.

Using Fractional Method for Finding Equivalency in Household Measurements

Points To Remember

Steps For Solving The Unknown Using Fractions And Cross Multiplication

1. Identify the unknown unit of measurement.

2. Find the known equivalent for the problem to be solved.

3. Write the known equivalents in a fraction on the left side of the equation.

4. Write the unknown desired equivalent in a fraction on the right side of the equation using x as the indication of the unknown.

5. Cross-multiply the numerators and denominators to solve for the unknown.

Another method of solving the unknown is to place the known equivalent and unknown equivalent into fractions and cross-multiply, as follows:

4 ft=_________in(Unknown equivalent)1 ft=12 in(Known equivalent)

NOTE: ft may be cancelled because both equivalents of the same measurement are known on the functional equation.

x in=12×4or48

Therefore,4 ft=48 in

OR

4 tbsp=___________tsp(Unknown equivalent)3 tsp=1 tbsp(Known equivalent)

NOTE: tbsp may be cancelled because both equivalents of the same measurement are known.

xtsp=3×4=12tsp

Therefore,4 tbsp=12 tsp.

Example 4-3

An infant is measured at 2′ ″. What would this be in inches? (1 ft = 12 inches)

To set up this problem, use a proportion as follows:

KnownUnknown1ft:12″::2 ft:xinches

x=24inches

Now add ″ to the 24″ as indicated in the problem.

So the infant’s length is ″.

OR

Known Unknown

1×xin=2×12orx=24in

24inches+112inches=2512inches

Example 4-4

Sally needs to take a teaspoon of medication. The only measuring spoon available is a tablespoon. How much medication should Sally place in the tablespoon for an approximation of each dose?

KnownUnknown1tbsp:3 tsp::x:1 tsp

3xtbsp=1 tbsp

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1. Assessment of Mathematical Calculation Skills Needed for Pharmacy Technicians
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