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:

< ?xml:namespace prefix = "mml" />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

x=13tbsp

OR

Known Unknown

3x=1 tbsp

x=13tbsp

 Tech Alert

The use of household measurement utensils provide only an approximation of a needed dose and may result in either an overdose or too little of the medication. When an approximate dose is given, therapy may be varied and may not provide the therapeutic results desired.

Points To Remember

The Household System

• The household system uses fractions and Arabic numerals.

• Teaspoon and tablespoon are common measures in household measures.

• For patient safety, household utensils should not be used except when absolutely necessary. Household utensils are only approximations. For correct dosing use the measuring device provided with the medication.

Practice Problems A

Calculate the following conversions. Show all of your calculations. Use the tables as provided in this section of text, using the correct indications for parts of a number if the answer is not a whole number.

1. 9 tsp = __________ tbsp

2. 39″ = __________ ft __________ ″

3. 2 qt = __________ gal

4. 3 tbsp = __________ oz

5. 6 oz = __________ c

6. 5 c = __________ oz

7. 15 tsp = __________ tbsp

8. 75 gtts = __________ tsp

9. 24 tbsp = __________ c

10. oz = __________ tsp

11. 4 c = __________ pt

12. 20 oz = __________ #

13. 4′ 6″ = __________ ″

14. 6′ 1″ = __________ ″

15. # = __________ oz

16. 5′ 10″ = __________ ″

17. tbsp = __________ tsp

18. tbsp = __________ gtts

19. 3 pt = __________ qt

20. 6 qt = __________ gal

21. 3 tsp = __________ gtts

22. 45 gtts = __________ tsp

23. 30 oz = __________ # (use decimal places to hundredths for this problem)

24. 24 oz = __________ c

25. 10 c = __________ oz

Practice Problems B

Patients will often use calibrated medication cups or oral syringes at home to take medications; however, these utensils may not be provided or may be misplaced so the pharmacy technician must have an understanding of conversions within household measurements. Convert the following problems to easier-to-use household measurements.

1. The physician orders  tsp of amoxicillin.

How many tablespoons would the patient take? __________

2. The physician orders 1 oz of milk of magnesia.

How many tablespoons are ordered? __________

3.  The physician orders 120 gtts of Rondec DM for a child.

How many teaspoonfuls would you give the child? __________

4.  A patient is to take 1 quart of Go-Lytely in preparation for x-rays.

How many ounces of the medication should the patient drink? __________

5. The physician tells the patient to drink at least 24 additional ounces of water a day.

How many cups of additional water would the patient need to drink to follow the physician’s order? __________

Learning Tip

When using ratio and proportion to convert either within the same measurement system or when converting between two measurement systems, place your known measurements first and then be sure to place the unknown measures in the same order.

Metric System of Measurement

The metric system of measurement is the most widely used throughout the world and is the most commonly used system for measuring medications and dosage. Most prescriptions are written in the metric system, and most liquid drugs are administered using this system. The U.S. Pharmacopeia names the metric system as the appropriate system for use on drug labels. The Metric Conversion Act of 1975 stated that the United States would convert to the use of the metric system, but the date for the completion of the conversion was not given. Transition to the metric system is evident in gauges, road signs, car speedometers, and other commercial products, but members of the U.S. public have not converted their thinking to the metric system in all areas such as height, weight, and length.

The metric system is based on units of 10 and uses decimals to move within the system. The basic measurements are gram for weight, liter for volume, and meter for length. In this system, prefixes for the base measurements are used to indicate the multiples or submultiples of the base that is being described, such as milli- (one thousandth of the base), micro- (one millionth of the base), and kilo- (1000 base units). These are the prefixes most commonly used, whereas centi- is one hundredth of a base and is the most commonly used with length. Deci- equals one tenth of the base, deka- is 10 times the base, and hecto- is 100 times the base.

Tech Note

A gram is about the weight of two large sized paper clips.

A liter is about the size of a quart container.

A meter is a little longer than a yardstick.

Labels in the metric system are shown in the appropriate metric unit. However, some labels still contain abbreviations that are found on The Joint Commission “Do Not Use” List, such as µg for microgram as found on the label for Lanoxin in Figure 4-2.

See Figure 4-3 for basic metric units with their prefixes and Tables 4-4 and 4-5 for a summary of the metric system and its equivalents.

Converting from Larger Metric Numbers to Smaller Metric Numbers

The metric system is easy for conversions from one unit to the next because multiples of 10 are the base for the system. The placement of the decimal point is based on moving from the different powers of 10 by moving the decimal point. When moving from a larger metric unit to a smaller one, move the decimal point to the right the number of times that the unit is larger than the smaller unit or multiply by the number of zeros in the equivalent (large to small → multiply). See Examples 4-5 and 4-6.

Example 4-5

1.2L=_______________mL

A liter is larger than a milliliter, so we must move the decimal from left to right. A milliliter has three decimal places to the right, so we want to move the decimal three places to the right or multiply by 1000.

1.2L=1200mL

Learning Tip

To go to the Smaller number, move the decimal to the Right. “R” and “S” are next to each other in the alphabet.

Example 4-6

5.4kg=_______________mg

5.4 kg=5,400,000 mg

Converting from a Smaller Metric Number to a Larger Metric Number

If the movement is from a smaller to larger unit, move the decimal point to the left the number of times the unit is smaller or divide by the number of zeros found in the desired equivalent (small to large ← divide). To change a kilogram to a milligram, a kilogram is larger than a milligram, so we must move the decimal to the left. A kilogram has six zeros when moving to a kilogram, so we want six places behind the decimal point. See Examples 4-7 and 4-8.

Learning Tip

To move from the smaller number to a Larger number, move the decimal to the Left. Both “Larger” and “Left” begin with “L”.

Example 4-7

5mg=_______________g

A milligram is smaller than a gram, so we move the decimal to the left by the number of zeros between a gram and a milligram (1 gram is equal to 1000 mg) or divide 5 mg by 1000 units.

Tech Note

Remember to always place a “0” in front of the decimal point if no number is otherwise present.

Example 4-8

500 g=_______________kg

A gram is smaller than a kilogram, so the decimal moves to the left. A kilogram is equal to 1000 grams or three zeros to the left of a gram.

Because the zeros behind a decimal that are not followed by a number or trailing zeros can be dropped, the problem answer is as follows:

500 g=0.500 kg=0.5 kg

Using a Mnemonic to Convert Within the Metric System

An easy way to calculate within the metric system is to use a mnemonic in which the first letters in the mnemonic is the first letter of a metric unit. This allows the moving of decimal places from the known unit to the desired unit without having to remember whether to multiply or divide for the correct answer.

To use Figure 4-4, circle the two letters on the metric line that are stated in the desired conversion. Place the given amount on the metric line with the decimal point in the correct place on the line. (Remember that the decimal point in a whole number follows the number.) Now place a decimal point directly behind the letter on the line for the desired placement value and add zeros under each letter of the metric scale using the mnemonic until the desired metric unit is reached. See Figure 4-3 for the basic units of measure.

Rules For Converting Within The Metric System Using The Mnemonic

• Using the mnemonic, construct the horizontal metric line from kilo- to micro- (K H D B D C M_ _M).

• Circle the known metric unit and the desired metric unit that are found in the problem.

• Place the decimal point of the known number in the correct place on the metric line.

• Place the decimal point of the unknown number in the correct place on the metric line.

• Fill in the spaces between the decimal points on the metric line with zeros.

• Avoid using decimals when whole numbers can be used (e.g., 0.5 g would be better expressed as 500 mg).

Example 4-9

500g=_______________kg

Hint: Remember that gram is a base unit.

(Move the decimal to the left to behind the kilogram unit and add a zero under the kilograms because grams are smaller than kilograms. The zeros are dropped because trailing zeros should be removed or mistakes in calculations and administration may occur.)

Example 4-10

5.4 kg=_______________mg

(Move the decimal to the right to behind the milligram unit because kilograms are larger than milligrams. Then add zeros under each unit that the decimal has been moved.)

Tech Note

When numbers in an answer are 10,000 or more, add commas as appropriate to avoid calculation mistakes.

Example 4-11

0.1mg=_______________gm

(Move the decimal to the left from behind the milligram to the gram. Notice that the decimal is behind the 0 in milligram and in front of the 1 because the unit is 0.1 mg. After placing the number correctly on the unit line and placing the decimal at the base for gram, add the proper number of zeros in front of the one for the number of units between the decimal points.)

 Tech Alert

The abbreviation “cc” is on the “Do Not Use” list because of the danger of reading the abbreviation as “00” (zeros); the unit mL should be used instead.

Practice Problems C

Complete the following problems by either using the number line of the mnemonic or by multiplying or dividing for the conversions within the metric system.

1. 2 L = __________ mL

2. 2.5 mg = __________ mcg

3. 4 kg = __________ g

4. 450 g = __________ kg

5. 0.5 L = __________ mL

6. 0.5 mg = __________ mcg

7. 0.5 mg = __________ g

8. 2.5 mL = __________ L

9. 50 mL = __________ L

10. 5.5 L = __________ mL

11. 1.5 g = __________ mg

12. 2.5 cm = __________ mm

13. 6.54 kg = __________ mg

14. 450 mm = __________ m

15. 25 mcg = __________ mg

16. 50.6 kg = __________ g

17. 10 L = __________ mL

18. 500 mL = __________ L

19. 3500 mL = __________ L

20. 0.0045 kg = __________ g

21. 0.3 mg = __________ mcg

22. 5 mL = __________ L

23. 58,400 mL = __________ L

24. 505 mL = __________ L

25. 300 mg = __________ mcg

26. A container of IV fluids contains liter. How many milliliters is this? __________

Hint: Change to a decimal first.

27. Amoxicillin is available as 250 mg/capsule.

How many grams of amoxicillin does each capsule contain? _____________________

28.  A tablet of digoxin contains 250 mcg.

How would this be written in mg? _____________________

29.  A physician orders 1 g of Cipro.

How many mg would the physician expect to be administered to the patient? __________

30.  A physician orders a thyroid replacement, Synthroid 0.175 mg.

How many micrograms would be given to the patient? _____________________

Apothecary System Of Measurement

Less often used and used only with pharmacology, the apothecary system is one of the oldest systems of measurement. First used by an apothecary (precursor to a pharmacist), this system is gradually being replaced with the metric system. As long as prescriptions are written in this system, the health care worker must be aware of its notations and rules.

The metric system is the preferred measurement system; however, the apothecary system can still be found on rare occasions, especially with older medications, such as Nitrostat as seen in Figure 4-5. Other places where apothecary measurements are found are syringes, such as minims (); drams () are found on medication-dispensing cups even though the use of these items and measurements are discouraged. These apothecary abbreviations are also found on the “Do Not Use List.”

In the apothecary system, lower case Roman numerals are used for expression of numbers below 10, rather than Arabic numerals found in the metric and household systems. The Roman numerals should be expressed with lines placed over numerals to tie these together such as , , , , and Arabic numerals may be used for numbers higher than 10, except with 20 () and 30 (), for which Roman numerals are required. Over the years, the use of the line over the Roman numeral has gradually diminished, but using it is the correct notation. The proper abbreviation is written first with Roman numerals placed to the right of the unit of measure—the opposite placement as found with metric and household. Most fractions are written using Arabic numbers such as or , except , which is abbreviated as . The abbreviation actually means “semis.” Also of importance is that decimals are not used with the apothecary system.

In ancient times, a minim (drop) of water was considered to weigh the same as a grain of wheat. Therefore the basic unit of liquid in the apothecary system is a minim () and the basic unit of weight is a grain (gr). See Table 4-6 for equivalents in the apothecary system.

TABLE 4.6

Equivalents in the Apothecary System

TYPE OF SUBSTANCE	ABBREVIATION	UNIT OF MEASURE	COMMON EQUIVALENTS
Volume/Liquid		minim	—
		fluid dram	lx (60)
		fluid ounce	viii (8)
Mass/Weight	gr	grain	—
		dram	gr lx (60)
		ounce	viii (8)
	#	pound	xii (12)*

^*Note that in the apothecary system a pound is only 12 ounces, but this not used on a regular basis in pharmacy calculations.

When notated in the apothecary system, the measurement is abbreviated and the amount drug always follows or is to the right (or behind) the abbreviated symbol (e.g., 5 oz would be written v, or 10 drams would be x).

As with household measurements, the use of ratio and proportion or fractional components can be used to make the conversion within the system.

Example 4-12

Known Unknown

NOTE: Remember that the apothecary system is written in Roman numerals, although you may decide to convert to Arabic numbers to compute the problem.

OR

Known Unknown

Review

Three measurement systems are used in practicing pharmacology. The household system is the most commonly used on a daily basis in our homes and is also the system used for giving liquid medications at home if the appropriate dispenser is not provided. However, using the household system provides only approximate measurements because of the difference in utensils; it may cause an inaccurate dose when used for administering medication. The metric system is used as a standard unit of measure throughout the world and is structured on base 10 or multiples of 10. Most medications are designated in the metric system today. The final system, rarely used today but found with some medications, is the apothecary system, which is based on grains for weight and minims, drams, and ounces for volume. Although this system is not popular and its use is being discouraged, these measurements are still seen occasionally with some medications. Because of the three systems, the measurements for length, weight, and volume must be learned for conversions that are discussed in the next chapter, where conversions among systems are often approximate conversions and not exact conversions as found in this chapter.

Ratio/proportion may be used for the calculation of changes within a system. With the metric system, the decimal may be moved to make the necessary conversion. Use the method that is best for you and use it consistently.