LEARNING OBJECTIVE: Recall the various pharmaceutical weight and measurement systems, and determine medication dosage by using the conversion process or the percentage and ratio calculations.
As you progress in your career as a Hospital Corpsman, you will be assigned duties in specialized departments throughout the hospital and especially aboard ship. Not only will your responsibilities increase, but your training will become more and more diversified.
One of the departments to which you may be assigned is the pharmacy, where you will assist in preparing and dispensing medicines. This section will give you a basic introduction to the field of pharmacy and help prepare you for these responsibilities.
METROLOGY AND CALCULATION
Metrology, called the arithmetic of pharmacy, is the science of weights and measures and its application to drugs, their dosage, preparation, compounding, and dispensing.
It is absolutely vital for medical technicians to thoroughly understand the principles and applications of metrology in pharmacy. Errors in this area endanger the health—even the life—of the patient.
The Metric System
The metric system is used for weighing and calculating pharmaceutical preparations. The metric system is becoming the accepted system throughout the world. Medical technicians need to be concerned primarily with the divisions of weight, volume, and linear measurement of the metric system. Each of these divisions has a primary or basic unit and is listed below:
By using the prefixes deka, hecto, and kilo for multiples of, respectively, ten, one hundred, and one thousand basic units, and the prefixes micro, milli, centi, and deci for oneten thousandth, one thousandth, onehundredth, and onetenth, respectively, you have the basic structure of the metric system. By applying the appropriate basic unit to the scale of figure 61, you can readily determine its proper terms. For example, using the gram as the basic unit of weight, we can readily see that 10 g equals 1 dekagram, 100 g equals 1 hectogram, and 1000 g is referred to as a kilogram. Conversely, going down the scale, 0.1 g is referred to as a decigram, 0.01 g is called a centigram, and 0.001 g is a milligram.
Figure 61.—Graph comparing the metric system with the decimal equivalent.
The Apothecary System
Although fast becoming obsolete, the apothecary system for weighing and calculating pharmaceutical preparations is still used and must be taken into consideration. It has two divisions of measurement: weight and volume. In this system, the basic unit of weight is the grain (abbreviated “gr”), and the basic unit of volume is the minim (abbreviated “m”).
GRAM METER LITER
The Avoirdupois System
The avoirdupois system is a system used in the United States for ordinary commodities. The basic units of the avoirdupois system are dram (27.344 grains), ounce (16 drams), and pound (16 ounces).
Table of Weights and Measures
See table 61, a table of weights and measures; study it thoroughly.
Table 61.—Measuring Equivalents
Converting Weights and Measures
Occasionally, there are times when it will be necessary to convert weights and measures from one system to another, either metric to apothecary or vice versa. Since patients can hardly be expected to be familiar with either system, always translate the dosage directions on the prescription into a household equivalent that they can understand. Household measurements are standardized, on the assumption that the utensils are common enough to be found in any home. Table 62 is a table of household measures, with their metric and apothecary equivalents.
Table 62.—Table of Metric Doses with Approximate Equivalents
NOTE

CONVERSION
As stated earlier, in the practice of pharmacy it may be necessary to convert from one system to another to dispense in their proper amounts the substances that have been ordered. Although the denominations of the metric system are not the same as the common systems, the Bureau of International Standards has established conversion standards that will satisfy the degree of accuracy required in almost any practical situation. Ordinary pharmaceutical procedures generally require something between two and threefigure accuracy, and the following tables of conversion (tables 63 and 64) are more than sufficient for practical use. Naturally, if potent agents are involved, you must use a more precise conversion factor for purposes of calculation.
Table 63.—Conversion Table for Weights and Liquid
PERCENTAGE CALCULATIONS
Percentage means “parts per hundred” or the expression of fractions with denominators of 100. Thus, a 10 percent solution maybe expressed as 10%, 10/100, 0.10, or 10 parts per 100 parts.
It is often necessary for the pharmacist to compound solutions of a desired percentage strength. Percentage in that respect means parts of active ingredient per 100 parts of total preparation.
Following are the three basic rules to remember in solving percentage problems:
To find the amount of the active ingredient when the percentage strength and the total quantity are known, multiply the total weight or volume by the percent (expressed as a decimal fraction)
.
3. To find the percentage strength when the amount of the active ingredient and the total quantity of the mixture are known, divide the weight or volume ofthe active ingredient by the total weight or volume of the mixture. Then multiply the resulting answer by 100 to convert the decimal fraction to percent.
ALTERNATE METHODS FOR SOLVING PERCENTAGE PROBLEMS
The alternate method for solving percentage problems, illustrated below, incorporates the three rules discussed above into one equation. This method is often preferred since it eliminates errors that may result from misinterpreting the values given in the problem.
A variation of the alternate percentage equation, illustrated below, uses “parts per hundred” instead of percent, with X used as the unknown.
RATIO AND PROPORTION CALCULATIONS
Ratio is the relationship of one quantity to another quantity of like value. Example ratios are 5:2, 4:1. These ratios are expressed as “5 to 2” and “4 to 1,” respectively. A ratio can exist only between values of the same kind, as the ratio of ercent to percent, grams to grams, dollars to dollars. In other words, the denominator must be constant.
Proportion is two equal ratios considered simultaneously. An example proportion is 1:3::3:9
This proportion is expressed as “1 is to 3 as 3 is to 9.” Since the ratios are equal, the proportion may also be written 1:3 = 3:9
Terms of Proportion
The first and fourth terms (the terms on the ends) are called the extremes. The second and third terms (middle terms) are called the means. In a proportion, the product of the means equals the product of the extremes; therefore, when three terms are known, the fourth (or unknown) term maybe determined.
Application of Proportion
The important factor when working proportions is to put the right values in the right places within the proportion. By following a few basic rules, you can accomplish this without difficulty and solve the problem correctly. In numbering the four positions of a proportion from left to right (i.e., first, second, third, and fourth, observe the following rules):
Ratio Solutions
Ratio solutions are usually prepared in strengths as follows: 1:10,1:150,1:1000,1:25000, etc., using even numbers to simplify the calculations. When a solution is made by this method, the first term of the ratio expresses the part of the solute (the substance dissolved in a solvent), while the second term expresses the total amount of the finished product.
Rules for solving ratiosolution problems are as follows:
W/W (weight/weight) solution: Divide the total weight (grams) of solution desired by the larger number of the ratio, and the quotient will be the number of grams of the solute to be used.
W/V (weight/volume) solution: Divide the total volume (in milliliters) of solution desired by the larger number of the ratio, and the quotient will be the number of grams of the solute needed.
V/V (volume/volume) Solution: Divide the total volume (in milliliters) of the solution desired by the larger number of the ratio, and the quotient will be the number of milliliters of the drug to be used.
Percentage solutions from stock and/or ratio solutions: