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10 Apothecary Measurement and Conversion

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**Student Learning Outcomes**

Convert among apothecary, household, and metric measurement systems Use the correct number formats for the measurement systems Properly format the answers After completing the tasks in this unit, you will be able to: Convert among apothecary, household, and metric measurement systems Use the correct number formats for the measurement systems Properly format the answers

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**Overview Purpose of this unit Bring together fundamental skills**

10-1 Purpose of this unit Bring together fundamental skills Fractions (1/2) Decimals (0.25) Ratio (2 : 7) Proportion ( ) Percents (25%) Apply these basics to health care This unit brings together the fundamental skills of the previous units and applies these basics to health care situations. Although you will learn new information in this unit, the processes for arriving at the correct answers depend on your ability to compute using fractions, decimals, ratios, proportions and, to a lesser degree, percents. This unit will cover apothecary measurements and two methods of converting among measurement systems. These fundamentals will help prepare you for math applications in the health care professions.

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**Overview Content of this unit Apothecary measurements**

10-1 Content of this unit Apothecary measurements Conversion among measurement systems This unit brings together the fundamental skills of the previous units and applies these basics to health care situations. Although you will learn new information in this unit, the processes for arriving at the correct answers depend on your ability to compute using fractions, decimals, ratios, proportions and, to a lesser degree, percents. This unit will cover apothecary measurements and two methods of converting among measurement systems. These fundamentals will help prepare you for math applications in the health care professions.

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**Apothecary System Apothecary measurement system—drug amounts**

10-1 Apothecary measurement system—drug amounts Weight “grains” Volume “minims” Relies on several number systems Lowercase Roman numerals Arabic numerals Fractions The apothecary system is an old measurement system originating in England. This system, which uses grains for weight and minims for volume, is used by physicians and pharmacists to calculate drug amounts. It relies on several number systems to denote measurements: lowercase Roman numerals, Arabic numerals, and fractions. Although this system is being replaced by metric units to make the measuring system more uniform and avoid medication errors, we discuss this system because you may encounter the apothecary units of measure, as some physicians still use this system as a matter of habit. So until the apothecary system is completing converted over to metric units, you may see labels, prescriptions, and doctors’ orders using some of these units.

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**Apothecary: Basic Rules**

10-1 Rule 1 Fractions of ½ may be written as ss Example: Nurse will give grains iss of medication to the patient. Rule 1 Fractions of ½ may be written as ss. Example: The nurse will give grains iss of medication to the patient. Rule 2 Lowercase Roman numerals used for amounts ≤ 10 and 20 and 30. Example: The doctor prescribed grains x (10) of the medication. Rule 3 Symbol placed before quantity (e.g., 7½ grains grains viiss). Example: The pharmacist prepared grains ivss of medication. Grains can also be abbreviated as “gr.” Remember that in metric and household measurements, the symbol follows the quantity: for example 25 milligrams, 3 cups,16-1/3 pounds. But in apothecary measurement, the symbol is placed before the quantity.

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**Apothecary: Basic Rules**

10-1 Rule 2 Lowercase Roman numerals used for amounts ≤ 10 and 20 and 30 Example: Doctor prescribed grains x (10) of the medication. Rule 1 Fractions of ½ may be written as ss. Example: The nurse will give grains iss of medication to the patient. Rule 2 Lowercase Roman numerals used for amounts ≤ 10 and 20 and 30. Example: The doctor prescribed grains x (10) of the medication. Rule 3 Symbol placed before quantity (e.g., 7½ grains grains viiss). Example: The pharmacist prepared grains ivss of medication. Grains can also be abbreviated as “gr.” Remember that in metric and household measurements, the symbol follows the quantity: for example 25 milligrams, 3 cups,16-1/3 pounds. But in apothecary measurement, the symbol is placed before the quantity.

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**Apothecary: Basic Rules**

10-1 Rule 3 Symbol placed before quantity (e.g., 7½ grains grains viiss) Example: Pharmacist prepared grains ivss of medication. Rule 1 Fractions of ½ may be written as ss. Example: The nurse will give grains iss of medication to the patient. Rule 2 Lowercase Roman numerals used for amounts ≤ 10 and 20 and 30. Example: The doctor prescribed grains x (10) of the medication. Rule 3 Symbol placed before quantity (e.g., 7½ grains grains viiss). Example: The pharmacist prepared grains ivss of medication. Grains can also be abbreviated as “gr.” Remember that in metric and household measurements, the symbol follows the quantity: for example 25 milligrams, 3 cups,16-1/3 pounds. But in apothecary measurement, the symbol is placed before the quantity.

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**APPROXIMATE CONVERSION**

Apothecary 10-1 Apothecary symbols Fluid ounce Grain TERM SYMBOL APPROXIMATE CONVERSION fluid ounce ℥ ℥ 1 = 6 teaspoons grain gr grain i = 60 milligrams You must memorize two common symbols in apothecary measurement: the symbol for fluid ounce and the symbol for grain.

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**Approximate Equivalents**

10-1 The equivalents are approximate. Rounded to nearest whole number Example: 1 gram = grains grains 15 Once you are familiar with these terms, symbols, and their equivalents, you will be ready to use these apothecary units in your conversions. This is a new concept for health care students to learn. We think of science and measurement as exact, but apothecary is a measurement system of approximate equivalents. Approximate equivalents come into play when you are converting among the measurement systems. Metric-to-metric or household-to-household measurement conversions usually can be done in exact measurements. In general, metric- or household-to-apothecary measurement conversions are done through approximate measures. The equivalents are called approximate because they are rounded to the nearest whole number. In exact measures, 1 gram is equivalent to grains ; however, the simple conversion in approximate equivalents used in health care is 1 gram = grains 15. To accomplish these conversions, you must memorize some of the approximate equivalents seen in this table. Let‘s review the table: 1 teaspoon = 5 milliliters 1 inch = 2.54 centimeters grain i = 60 or 65 milligrams 1 kilogram = 2.2 pounds grain i = 1 drop 1 teaspoon = 60 drops 1 pint = 2 cups ℥ 1 = 6 teaspoons 1 quart = ℥ 32 ℥ 1 = 2 tablespoons 1 quart = 1 liter ℥ 1 = 30 milliliters 1 cup = 240−250 milliliters Notice that the conversions in the table are set up so that the unit (1) elements are all on the left and that these will be placed on top of the known part of the ratio and proportion equation. This simplifies the learning process, expedites learning, and helps recall these conversions. 10

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**Approximate Equivalents**

10-1 The equivalents are approximate APPROXIMATE EQUIVALENTS 1 teaspoon = 5 milliliters 1 inch = 2.54 centimeters grain i = 60 or 65 milligrams 1 kilogram = 2.2 pounds grain i = 1 drop 1 teaspoon = 60 drops 1 pint = 2 cups ℥ 1 = 6 teaspoons 1 quart = ℥ 32 ℥ 1 = 2 tablespoons 1 quart = 1 liter ℥ 1 = 30 milliliters 1 cup = 240−250 milliliters Once you are familiar with these terms, symbols, and their equivalents, you will be ready to use these apothecary units in your conversions. This is a new concept for health care students to learn. We think of science and measurement as exact, but apothecary is a measurement system of approximate equivalents. Approximate equivalents come into play when you are converting among the measurement systems. Metric-to-metric or household-to-household measurement conversions usually can be done in exact measurements. In general, metric- or household-to-apothecary measurement conversions are done through approximate measures. The equivalents are called approximate because they are rounded to the nearest whole number. In exact measures, 1 gram is equivalent to grains ; however, the simple conversion in approximate equivalents used in health care is 1 gram = grains 15. To accomplish these conversions, you must memorize some of the approximate equivalents seen in this table. Let‘s review the table: 1 teaspoon = 5 milliliters 1 inch = 2.54 centimeters grain i = 60 or 65 milligrams 1 kilogram = 2.2 pounds grain i = 1 drop 1 teaspoon = 60 drops 1 pint = 2 cups ℥ 1 = 6 teaspoons 1 quart = ℥ 32 ℥ 1 = 2 tablespoons 1 quart = 1 liter ℥ 1 = 30 milliliters 1 cup = 240−250 milliliters Notice that the conversions in the table are set up so that the unit (1) elements are all on the left and that these will be placed on top of the known part of the ratio and proportion equation. This simplifies the learning process, expedites learning, and helps recall these conversions. HINT: THE CONVERSIONS ARE SET UP WITH THE UNITS (1) ON THE LEFT.

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**Conversions Conversions Problem: Set up known quantity**

10-2 KNOWN UNKNOWN Conversions Set up known quantity Set up unknown quantity Solve with proportion format Problem: How many milliliters are in 2½ ounces? These conversions are accomplished by setting up the known and unknown quantities in proportion format. Use the following example as your guide: Problem: How many milliliters are in 2-1/2 ounces? To solve with proportion format: Set up the known conversion on the left, and the unknown on the right in proportion format. 1 ounce over 30 milliliters = 2-1/2 ounces over how many milliliters? Cross multiply 30 by 2-1/2 to get 75. Now divide this 75 by the remaining number (1). Shortcut: Remember that any number divided by 1 is itself. Thus the answer is 75 milliliters.

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**Conversion Example Problem: Convert 48 milligrams to grains 10-2 Hint:**

Grains are in whole numbers and/or fractions. Milliliters are in whole numbers and decimals. Let’s work through another example. Convert 48 milligrams to grains. Set up the proportion with the known on the left and the unknown on the right. Grain i over 60 or 65 milligrams = how many grains over 48 milligrams? Cross multiply 1 by 48 to get 48. Now divide 48 by the remaining number (60). Note: Instead of dividing this out and getting a decimal, we will leave the division as a fraction because grains are in whole numbers or fractions (see the hint on the slide). So now we have 48 over 60, which reduces to 4 over 5 (both numbers divide by 12 when we write out the factors) Our answer is 4/5 grains, more properly written as “grains 4/5.”

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**Using “Dimensional Analysis”**

10-2 Problem: How many milliliters are in 2½ ounces? The “Dimensional Analysis Method” is a widely used alternative to the ratio, proportion, and dosage formula methods. There are no formulas to memorize. It is a problem-solving method that uses the fact that any number or expression can be multiplied by 1 without changing its value. Remember that in dimensional analysis, you can cancel like units if they appear in both the numerator and the denominator. Let’s work through an example. We’ll use the one we just did: How many milliliters are in 2½ ounces? Place the unit of measure on one side of the equation: “? milliliters =” Use the conversion factor most appropriate to the problem. Place the factor of the unit of measure for the answer on top and the unit that you are converting to on the bottom as the denominator. ? milliliters = 30 milliliters over 1 ounce Hint: The first factor on the right side of the equation will have the same unit of measure as the unknown that is being solved for. Multiply the first factor by the given information from the problem. So add to the problem: “times 2½ ounces over 1” Cancel the like units (in this case the ounces on top and bottom). Remember that you can cancel units only if the same unit appears on both top and bottom. And both terms are now over 1, and we know that anything divided by 1 is itself, so we can ignore the 1s in the denominators. That leaves us with 30 milliliters times 2½ Now solve by multiplying straight across with what’s left: 30 milliliters times 2½. The answer is 75 milliliters. Why? 30 times 2½ is 75. Milliliters is the only unit left.

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**“Do Not Use” List “Do Not Use” List of medical abbreviations**

10-3 “Do Not Use” List of medical abbreviations To eliminate use of problematic abbreviations To prevent misreading To reduce risk To prevent errors in patient care Example: microgram = mcg Formerly: microgram = μg In 2004, the Joint Commission created an official “do not use” list of medical abbreviations to meet a National Patient Safety Goal. Review this list regularly to reduce risk and prevent errors in patient care. Problematic abbreviations can be misread. For example, micrograms used to be written as μg, which could be misread. The preferred form is now “mcg”.

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**Multiple Conversions Work with the same units before changing.**

10-2 Work with the same units before changing. Why? Only one math setup per problem Use standard conversion equivalents Example: grams = grains _____ grams becomes 0.1 milligrams When completing multiple conversions, it is best to work within the same unit of measure before changing to another unit of measure. For example, do all of the metric conversions, then move to the grain conversions; or make the grain-to-metric conversion into milligrams, and then convert from milligrams to grams or micrograms. By doing so, you will have only one math setup per problem. Use the standard conversion equivalents to make the conversions. Let’s look at our example grams = how many grains? You may need to convert twice to get to a known conversion. First, convert from grams to milligrams: grams becomes 0.1 milligrams (move the decimal three spaces to the right) Then, set up with known equivalents for the conversion: gr i over 60 mg = how many gr over 0.1 mg? Convert the 0.1 to a fraction (1/10) to ensure the proper format in the final answer—remember that grains is in whole numbers and fractions (not decimals). Now we have gr i over 60 mg = how many gr over 1/10 mg Now let’s work the problem (on the next slide).

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**Working the Problem (continued)**

10-2 Working our problem, we carry the setup over from the previous slide. Cross multiply i (which is 1) times 1/10 to get 1/10. Then divide this 1/10 by the remaining number (60), which is the same as 60/1. Remember that to divide fractions, you take the inverse of the second fraction and change the operator. So now we have 1/10 × 1/60. Multiplying straight across, we get 1/600. The final answer is “grains 1/600.”

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**Converting Liquid Equivalents**

10-1 Method Use ratio and proportion (or dimensional analysis) Rely on conversion charts and memorized equivalents You will convert liquid equivalents in the same manner, using ratio and proportion or dimensional analysis. You will need a wider range of conversions to convert liquid equivalents. Rely on the conversion charts, but work toward memorizing these equivalents so that you can efficiently apply them. We see the “approximate equivalents” chart we saw before.

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**Converting Liquid Equivalents**

10-1 APPROXIMATE EQUIVALENTS 1 teaspoon = 5 milliliters 1 inch = 2.54 centimeters grain i = 60 or 65 milligrams 1 kilogram = 2.2 pounds grain i = 1 drop 1 teaspoon = 60 drops 1 pint = 2 cups ℥ 1 = 8 teaspoons 1 quart = ℥ 32 ℥ 1 = 2 tablespoons 1 quart = 1 liter ℥ 1 = 30 milliliters 1 cup = 240−250 milliliters You will convert liquid equivalents in the same manner, using ratio and proportion or dimensional analysis. You will need a wider range of conversions to convert liquid equivalents. Rely on the conversion charts, but work toward memorizing these equivalents so that you can efficiently apply them. We see the “approximate equivalents” chart we saw before.

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**Guidelines for Rounding**

10-3 Place a 0 in the whole number place. Examples: 0.5 gram, 0.25 milligram, microgram Round decimals to the correct place value. The metric system is used to measure liquids, weights, and medicine. Rounding is used to ensure proper dosing. To assist in this process, follow these guidelines: Any decimal number that stands alone without a whole number must have a 0 placed in the whole number place. This is the standard way of noting a decimal number that does not have a whole number with it. It also helps ensure reading and interpreting the number correctly. Round decimals to the correct place value. This is somewhat dependent on your profession; however, some general guidelines exist. For example, kilogram and degrees in Celsius and Fahrenheit are placed in tenths. Multi-step problems require that you convert between number systems, especially between fractions and decimals. If the drug measurement is in metrics (milligram, gram, microgram), the solution to the problem must be in decimals. There are no fractions in the metric system. Therefore, ¼ milligram is stated as 0.25 milligram. Do not over round. In medications, a small amount of medication can be critical in dosing. If you begin to round as you set up the problem, you may round again when you finalize the problem and this can skew the dosage amount. A good rule of thumb is to round only when you reach your final answer. Of note is pediatric doses, which are rounded down, not rounded up to avoid over-dosing. The same principle is used with high-alert drugs with adults.

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**Guidelines for Rounding**

10-3 Use the proper number system (convert if needed). Example: ¼ milligram is stated as 0.25 milligram. Do not over-round (round at the end). The metric system is used to measure liquids, weights, and medicine. Rounding is used to ensure proper dosing. To assist in this process, follow these guidelines: Any decimal number that stands alone without a whole number must have a 0 placed in the whole number place. This is the standard way of noting a decimal number that does not have a whole number with it. It also helps ensure reading and interpreting the number correctly. Round decimals to the correct place value. This is somewhat dependent on your profession; however, some general guidelines exist. For example, kilogram and degrees in Celsius and Fahrenheit are placed in tenths. Multi-step problems require that you convert between number systems, especially between fractions and decimals. If the drug measurement is in metrics (milligram, gram, microgram), the solution to the problem must be in decimals. There are no fractions in the metric system. Therefore, ¼ milligram is stated as 0.25 milligram. Do not over-round. In medications, a small amount of medication can be critical in dosing. If you begin to round as you set up the problem, you may round again when you finalize the problem, and this can skew the dosage amount. A good rule of thumb is to round only when you reach your final answer. Of note is pediatric doses, which are rounded down, not up, to avoid overdosing. The same principle is used with high-alert drugs with adults. MATH SENSE: Correct formats mean correct answers!

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