pharmacy calculations

CHAPTER 5: PHARMACY CALCULATIONS 1

5Learning Objectives

After completing thischapter, the reader will beable to

1. Calculate conversionsbetween differentnumbering and measur-ing systems.

2. Calculate medicationdoses from variousmedication dilutions.

3. Calculate and defineosmolarity, isotonicity,body surface area, andflow rates.

4. Calculate and definearithmetic mean,median, and standarddeviation.

Review of Basic Mathematics

NumeralsA numeral is a word or a sign, or a group of words or signs, that ex-presses a number.

Kinds of NumeralsArabic

Examples: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9Roman

In pharmacy practice, Roman numerals are used only to denotequantities on prescriptions.

ss or ss = 1/2 L or l = 50I or i = 1 C or c = 100V or v = 5 D or d = 500X or x = 10 M or m = 1000It is important to note that when a smaller Roman numeral (e.g., “I”)

is placed before a larger Roman numeral (e.g., “V”), the smaller Romannumeral is subtracted from the larger Roman numeral. Conversely, when asmaller Roman numeral is placed after a larger one, the smaller one isadded to the larger.

Example 1: I = 1 and V = 5; therefore, IV = 4 because 5 – 1 = 4.Example 2: I = 1 and V = 5; therefore, VI = 6 because 5 + 1 = 6

Problem Set #1Convert the following Roman numerals to Arabic numerals:

a. ii = ___ b. DCV = ___ c. xx = ___d. iii = ___ e. vii = ___ f. iv = ___

Pharmacy CalculationsGERALD A. STORM, REBECCA S. KENTZEL

Most calculations pharmacy technicians and pharmacists use involve

basic math; however, basic math is easily forgotten when it is not used

routinely. This chapter reviews the fundamentals of calculations and how

those calculations are applied in pharmacy.

2 MANUAL FOR PHARMACY TECHNICIANS

g. IX = ___ h. xv = ___ i. xi = ___j. MXXX = ___ k. xiv = ___ l. xvi = ___

NumbersA number is a total quantity or amount that is made ofone or more numerals.

Kinds of NumbersWhole Numbers

Examples: 10, 220, 5, 19Fractions

Fractions are parts of whole numbers.Examples: 1/4, 2/7, 11/13, 3/8Always try to express a fraction in its simplest

form.Examples: 2/4 = 1/2; 10/12 = 5/6; 8/12 = 2/3The whole number above the fraction line is called

the numerator, and the whole number below thefraction line is called the denominator.Mixed NumbersThese numbers contain both whole numbers andfractions.

Examples: 1 1/2, 13 3/4, 20 7/8, 2 1/2Decimal NumbersDecimal numbers are actually another means of writingfractions and mixed numbers.

Examples: 1/2 = 0.5, 1 3/4 = 1.75Note that you can identify decimal numbers by the

period appearing somewhere in the number. Theperiod in a decimal number is called the decimal point.

The following two points about zeros in decimalnumbers are VERY important:

1. Do NOT write a whole number in decimalform.In other words, when writing a whole number,avoid writing a period followed by a zero (e.g.,5.0). Why? Because periods are sometimes hardto see, and errors may result from misreadingthe number. For example, the period in 1.0 maybe overlooked, and the number could appear tobe 10 instead, causing a 10-fold dosing error,which could kill someone.

2. On the contrary, when writing a fraction in itsdecimal form, always write a zero before theperiod.Why? Once again, periods are sometimesdifficult to see, and .5 may be misread as 5.

However, if the period in 0.5 were illegible, thezero would alert the reader that a period issupposed to be there.

Working with Fractions and DecimalsPlease note that this section is meant to be only a basicoverview. A practicing pharmacy technician shouldalready possess these fundamental skills. The problemsand examples in this section should serve as buildingblocks for all calculations reviewed later in this chapter.If you do not know how to do these basic functions,you need to seek further assistance.

Review of Basic Mathematical FunctionsInvolving FractionsWhen adding, subtracting, multiplying, or dividingfractions, you must convert all fractions to a commondenominator. Also, when working with fractions, besure that you express your answer as the smallestreduced fraction (i.e., if your answer is 6/8, reduce itto 3/4).

AdditionUse the following steps to add 3/4 + 7/8 + 1/4.

1. Convert all fractions to common denominators.3/4 × 2/2 = 6/81/4 × 2/2 = 2/8

2. Add the fractions.6/8 + 7/8 + 2/8 = 15/8

3. Reduce to the smallest fraction.15/8 = 1 7/8

SubtractionUse the following steps to subtract 7/8 – 1/4.

1. Convert the fractions to common denominators.1/4 × 2/2 = 2/8

2. Subtract the fractions.7/8 – 2/8 = 5/8

MultiplicationUse the following steps to multiply 1/6 × 2/3.

When multiplying and dividing fractions, you doNOT have to convert to common denominators.

1. Multiply the numerators: 1 × 2 = 22. Multiply the denominators: 6 × 3 = 183. Express your answer as a fraction: 2/184. Be sure to reduce your fraction: 2/18 = 1/9


DivisionUse the following steps to divide 1/2 by 1/4.

Once again, you do NOT have to convert tocommon denominators.

To divide two fractions, the first fraction must bemultiplied by the inverse (or reciprocal) of the secondfraction:

1/2 ÷ 1/4 is the same as 1/2 × 4/11. Multiply the fractions.

1/2 × 4/1 = 4/22. Reduce to lowest fraction.

4/2 = 2

Review of Basic Mathematical FunctionsInvolving DecimalsAs with fractions, when adding, subtracting, multiply-ing, or dividing decimals, all units (or terms) must bealike.

AdditionRemember to line up decimal points when adding orsubtracting decimal numbers.

Add the following: 0.1 + 124.7Add the terms by lining up the decimal points:

0.1+ 124.7 124.8

SubtractionSubtract the following: 2100 – 20.5

Subtract the terms by lining up the decimal points:2100.0– 20.52079.5

MultiplicationWhen multiplying decimal numbers, the number ofdecimal places in the product must equal the totalnumber of decimal places in the numbers multiplied, asshown below.

Multiply the following: 0.6 × 24In this example, there is a total of one digit to the

right of the decimal point in the numbers beingmultiplied, so the answer will have one digit to theright of the decimal point.

Answer: 0.6 × 24 = 14.4

DivisionThe dividend is the number to be divided, and thedivisor is the number by which the dividend is divided.When dividing decimal numbers, move the divisor’sdecimal point to the right to form a whole number.Remember to move the dividend’s decimal point thesame number of places to the right. When using longdivision, place the decimal point in the answer imme-diately above the dividend’s decimal point.

Divide the following: 60.75 ÷ 4.5Move the decimal points: 607.5 ÷ 45Answer: 607.5 ÷ 45 = 13.5

Converting Fractions to Decimal NumbersTo convert a fraction to a decimal, simply divide thenumerator by the denominator.

For example, 1/2 = one divided by two = 0.5

Converting Mixed Numbers to DecimalNumbersThis process involves the following two steps:

1. Write the mixed number as a fraction.Method: Multiply the whole number and thedenominator of the fraction. Add the product(result) to the numerator of the fraction, keepingthe same denominator.Example: 2 3/4 = two times four plus three overfour = 11/4

2. Divide the numerator by the denominator.Example: 11/4 = eleven divided by four = 2.75

An alternate method involves the following threesteps:

1. Separate the whole number and the fraction.Example: 2 3/4 = 2 and 3/4

2. Convert the fraction to its decimal counterpart.Example: 3/4 = three divided by four = 0.75

3. Add the whole number to the decimal fraction.Example: 2 plus 0.75 = 2.75

Converting Decimal Numbers to MixedNumbers or FractionsTo convert decimal numbers to mixed numbers orfractions, follow these three steps:

1. Write the decimal number over one, dividing itby one. (Remember that dividing any number byone does not change the number.)


Example: 3.5 = 3.5/12. Move the decimal point in the numerator as

many places to the right as necessary to form awhole number. Then move the decimal point inthe denominator the same number of places.Example: Because there is only one digit follow-ing the decimal point in 3.5, move the decimalpoint one place to the right in both the numera-tor and the denominator: 3.5/1 = 35/10.

Remember that the number will remain the sameas long as you do exactly the same things to thenumerator and the denominator. You also have toremember that the decimal point of a whole numberalways follows the last digit.

3: Simplify the fraction.Example: 35/10 = 7/2 = 3 1/2

Problem Set #2Convert the following fractions to decimal numbers:

a. 1/2 b. 3/4 c. 1 d. 2/5e. 1/3 f. 5/8 g. 50/100 h. 12/48i. 11/2 j. 2 2/3 k. 5 1/4 l. 3 4/5Convert the following decimal numbers to fractions

or mixed numbers:m. 0.25 n. 0.4 o. 0.75 p. 0.35q. 2.5 r. 1.6 s. 3.25 t. 0.33

PercentagesPercentage means “by the hundred” or “in a hundred.”Percents (%) are just fractions, but fractions with a setdenominator. The denominator is always one hundred(100).

Example: “50%” means “50 in a hundred” or“50/100” or “1/2”

Converting Percentages to FractionsWrite the number preceding the percent sign over 100and simplify the resulting fraction.

Example: 25% = 25/100 = 1/4

Converting Fractions to PercentagesConvert the fraction to one in which the denominatoris a hundred. This is easiest when the fraction is in theform of a decimal. Follow these four steps:

1. Write the fraction in its decimal form.Example: 3/4 = three divided by four = 0.75

2. Write the decimal over one.Example: 0.75/1

3. To obtain 100 as the denominator, move thedecimal point two places to the right. To avoidchanging the number, move the decimal pointtwo places to the right in the numerator as well.Example: 0.75/1 = 75/100

4. Because you already know that “out of a hun-dred” or “divided by a hundred” is the same aspercent, you can write 75/100 as 75%.

Concentration Expressed as a PercentagePercent weight-in-weight (w/w) is the grams of adrug in 100 grams of the product.Percent weight-in-volume (w/v) is the grams of adrug in 100 ml of the product.Percent volume-in-volume (v/v) is the millilitersof drug in 100 ml of the product.

The above concentration percentages will bediscussed in further detail a little later in this chapter.

Problem Set #3Convert the following percentages to fractions (remem-ber to simplify the fractions):

a. 23% b. 67% c. 12.5% d. 50%

e. 66.7% f. 75% g. 66% h. 40%

i. 100% j. 15%

Convert the following fractions to percentages:k. 1/2 l. 1/4 m. 2/5 n. 6/25

o. 4/100 p. 0.5 q. 0.35 r. 0.44

s. 0.57 t. 0.99

Units of Measure

Metric SystemThe metric system is based on the decimal system, inwhich everything is measured in multiples or fractionsof 10. Appendix 5-1 lists the conversion charts re-viewed on the following pages.

Standard MeasuresThe standard measure for length is the meter; thestandard measure for weight is the gram; and thestandard measure for volume is the liter.

PrefixesThe prefixes below are used to describe multiples or


fractions of the standard measures for length, weight,and volume.Latin Prefixes

micro- (mc): 1/1,000,000 = 0.000001milli- (m): 1/1000 = 0.001centi- (c): 1/100 = 0.01deci- (d): 1/10 = 0.1Note that Latin prefixes denote fractions.

Greek Prefixesdeca- (da): 10hecto- (h): 100kilo- (k): 1000mega- (M): 1,000,000Note that Greek prefixes denote multiples.

Prefixes with Standard MeasuresLength

The standard measure is the meter (m).1 kilometer (km) = 1000 meters (m)0.001 kilometer (km) = 1 meter (m)1 millimeter (mm) = 0.001 meter (m)1000 millimeters (mm) = 1 meter (m)1 centimeter (cm) = 0.01 meter (m)100 centimeters (cm)= 1 meter (m)

VolumeThe standard measure is the liter (L).1 milliliter (ml) = 0.001 liter (L)1000 milliliters (ml) = 1 liter (L)1 microliter (mcl) = 0.000001 liter (L)1,000,000 microliters (mcl) = 1 liter (L)1 deciliter (dl) = 0.1 liter (L)10 deciliters (dl) = 1 liter (L)

WeightThe standard measure is the gram (g).1 kilogram (kg) = 1000 grams (g)0.001 kilogram (kg) = 1 gram (g)1 milligram (mg) = 0.001 gram (g)1000 milligrams (mg) = 1 gram (g)1 microgram (mcg) = 0.000001 gram (g)1,000,000 micrograms (mcg) = 1 gram (g)

Apothecary SystemThe apothecary system was developed after the Avoir-

dupois system (see below) to enable fine weighing ofmedications. Today, the apothecary system is used onlyfor a few medications, such as aspirin, acetaminophen,and phenobarbital.

WeightThe standard measure for weight is the grain (gr).Pound Ounces Drams Scruples Grains1 = 12 = 96 = 288 = 5760

1 = 8 = 24 = 480 1 = 3 = 60

1 = 20

VolumeThe standard measure for volume is the minim (m.).Gallons Pints Fluid ounces Fluid drams Minims1 = 8 = 128 = 1024 = 61,440

1 = 16 = 128 = 7,680 1 = 8 = 480

1 = 60

Avoirdupois SystemThis system is used mainly in measuring the bulkmedications encountered in manufacturing. Be sure tonote that the pounds-to-ounces equivalent is differentin the apothecary and avoirdupois systems. Theavoirdupois system is most commonly used to measureweight, and the apothecary system is most commonlyused to measure volume. Be sure also to note thedifference in symbols used for the two systems. Inaddition, note that a fluid ounce, which measuresvolume, is often mistakenly shortened to an “ounce,”which is actually a measure of weight. Because ouncesmeasure weight, pay close attention to the measure youare working with and convert accordingly.

WeightThe standard measure for weight is the grain (gr).

Pound Ounces Grains(lb) (oz) (gr)1 = 16 = 7000

1 = 437.5

Household SystemThe household system is the most commonly usedsystem of measuring liquids in outpatient settings. Themeasuring equipment usually consists of commonlyused home utensils (e.g., teaspoons, tablespoons).


1 teaspoonful (tsp) = 5 ml1 dessertspoonful = 10 ml1 tablespoonful (TBS) = 15 ml = 0.5 fluid ounces (fl oz)1 wineglassful = 60 ml = 2 fl oz1 teacupful = 120 ml = 4 fl oz1 glassful/cupful = 240 ml = 8 fl oz3 tsp = 1 TBS2 TBS = 1 fl oz8 fl oz = 1 cup2 cups = 1 pint (pt)2 pt = 1 quart (qt)4 qt = 1 gallon (gal)The term drop is commonly used; however, caution

should be exercised when working with this measure,especially with potent medications. The volume of adrop depends not only on the nature of the liquid butalso on the size, shape, and position of the dropper. Toaccurately measure small amounts of liquid, use a 1-mlsyringe (with milliliter markings) instead of a dropper.Eye drops are an exception to this rule; they arepackaged in a manner to deliver a correctly sizeddroplet.

Problem Set #4Fill in the blanks:

a. 1 liter (L) = _______________ mlb. 1000 g = _______________ kgc. 1 g = _______________ mgd. 1000 mcg = _______________ mge. 1 TBS = _______________ tspf. 1 TBS = _______________ mlg. 240 ml = _______________ cupfulsh. 1 cup = _______________ mli. 15 ml = _______________ TBSj. 1 tsp = _______________ mlk. 240 ml = _______________ TBSl. 1 pt = _______________ mlm. 1 fl oz = _______________ TBSn. 1 qt = _______________ pt

Equivalencies Between SystemsThe apothecary, avoirdupois, and household systemslack a close relationship among their units. For thisreason, the preferred system of measuring is the metric

system. The table of weights and measures below givesthe approximate equivalencies used in practice.

Length Measures1 meter (m) = 39.37 (39.4) inches (in)1 inch (in) = 2.54 centimeters (cm)

Volume Measures1 milliliter (ml) = 16.23 minims1 fluid ounce (fl oz) = 29.57 (30) milliliters (ml)1 liter (L) = 33.8 fluid ounces (fl oz)1 pint (pt) = 473.167 (480) milliliters (ml)1 gallon (gal) = 3785.332 (3785) milliliters (ml)

Weight Measures1 kilogram (kg) = 2.2 pounds (lb)1 pound (avoir) (lb) = 453.59 (454) grams (g)1 ounce (avoir) (oz) = 28.35 (28) grams (g)1 ounce (apoth) (oz) = 31.1 (31) grams (g)1 gram (g) = 15.432 (15) grains (gr)1 grain (gr) = 65 milligrams (mg)1 ounce (avoir) (oz) = 437.5 grains (gr)1 ounce (apoth) = 480 grains (gr)

Temperature ConversionTemperature is always measured in the number ofdegrees centigrade (°C), also known as degrees Celsius,or the number of degrees Fahrenheit (°F). The follow-ing equation shows the relationship between degreescentigrade and degrees Fahrenheit: [9(°C)] = [5(°F)] –160°

Example: Convert 110°F to °C.[9(°C)] = [5(110°F)] – 160°°C = (550 – 160)/9°C = 43.3°

Example: Convert 15°C to °F[9(15°C)] = [5(°F)] – 160°(135 + 160)/5 = °F59° = °F

Conversion Between SystemsTo find out how many kilograms are in 44 lbs, followthese three steps:

1. Write down the statement of equivalency betweenthe two units of measure, making sure that theunit corresponding with the unknown in the


question is on the right.

2.2 lbs = 1 kg2. Write down the problem with the unknown

underneath the equivalency.

Equivalency: 2.2 lbs = 1 kg

Problem: 44 lbs = ? kg

3: Cross multiply and divide.

1 times 44 divided by 2.2 = [(1 × 44) / 2.2] =20 kg

Determining Body Surface AreaThe Square Meter Surface Area (Body Surface Area, orBSA) is a measurement that is used instead of kilo-grams to estimate the amount of medication a patientshould receive. BSA takes into account the patient’sweight and height. BSA is always expressed in meterssquared (m2) and is frequently used to dose chemo-therapy agents. When using the equation below, unitsof weight (W) should be kilograms (kg) and height (H)should be centimeters. The following equation is usedto determine BSA:

BSA=(W0.5378) × (H0.3964) × (0.024265)

Now, using the formula, follow these three steps tocalculate the BSA of a patient who weighs 150 poundsand is 5 feet 8 inches tall.

1. Convert weight to kilograms.

150 lb 68.22.2 lb/kg

= kg

2. Convert height to centimeters.

5 feet × 12 inches/foot = 60 inches

+ 8 inches = 68 inches

68 inches × 2.54 cm/inch = 172.7 cm

3. Insert the converted numbers into the formula.BSA = (W0.5378) × (H0.3964) × 0.024265

BSA = (68.20.5378) × (172.70.3964) × 0.024265

BSA = (9.69) × (7.71) × 0.024265BSA = 1.81m2

Problem Set #5Convert or solve the following:

a. 30 ml = _____ fluid ouncesb. 500 mg = _____ gc. 3 teaspoons = _____ fluid ouncesd. 20 ml = _____ teaspoons

e. 3.5 kg = _____ gf. 0.25 mg = _____ gg. 1500 ml = _____ Lh. 48 pints = _____ gallonsi. 6 gr = _____ mgj. 120 lb = _____ kgk. 3 fluid ounces = _____ mll. 72 kg = _____ poundsm. 946 ml = _____ pintsn. 800 g = _____ lbo. 3 tsp = _____ millilitersp. 2 TBS = _____ fluid ouncesq. 2 TBS = _____ mlr. 2.5 cups = _____ fl ozs. 0.5 gr = _____ mgt. 0.5 L = _____ mlu. 325 mg = _____ grv. 2 fl oz = _____ TBSw. 60 ml = _____ fl ozx. 144 lb = _____ kgy. 1 fl oz = _____ tspz. 4 tsp = _____ mlaa. 83°F = _____ °Cbb. –8°F = _____ °Ccc. 5°C = _____ °Fdd. 32°C = _____ °Fee. What is the BSA of a patient who weighs 210

pounds and is 5 feet 1 inch tall?

Ratio and ProportionA ratio states a relationship between two quantities.

Example: 5 g of dextrose in 100 ml of water (thissolution is often abbreviated “D5W”).A proportion is two equal ratios.Example: 5 g of dextrose in 100 ml of a D5Wsolution equals 50 g of dextrose in 1000 ml of aD5W solution; or

5 g 50 g100 ml 1000 ml

=

A proportion consists of two unit (or term) types(e.g., kilograms and liters, or milligrams and millili-ters). If you know three of the four terms, you cancalculate the fourth term.


Problem Solving by the Ratio and ProportionMethodThe ratio and proportion method is an accurate andsimple way to solve some problems. To use thismethod, you should learn how to arrange the termscorrectly, and you must know how to multiply anddivide.

There is more than one way to write a proportion.The most common is the following:

Term #1 Term #3Term #2 Term #4

=

This expression is read Term #1 is to Term #2 asTerm #3 is to Term #4.

By cross multiplying, the proportion can now bewritten as:

(Term #1) × (Term #4) = (Term #2) × (Term #3)Example 1: How many grams of dextrose are in 10

ml of a solution containing 50 g of dextrose in100 ml of water (D50W)?

1. Determine which is the known ratio and whichis the unknown ratio. In this example, the knownratio is “50 g of dextrose in 100 ml of solution.”The unknown ratio is “X g of dextrose in 10 mlof solution.”

2. Write the unknown ratio (Terms #1 and #2) onthe left side of the proportion. Be sure theunknown term is on the top.

g Term #310 ml Term #4X =

3. Write the known ratio (Terms #3 and #4) on theright side of the proportion. The units of bothratios must be the same—the units in thenumerators and the units in the denominatorsmust match. In this case, that means grams inthe numerator and milliliters in the denominator.If units of the numerators or the denominatorsdiffer, then you must convert them to the sameunits.

g 50 g10 ml 100 mlX =

4. Cross multiply.X g × 100 ml = 50 g × 10 ml

5. Divide each side of the equation by the knownnumber on the left side of the equation. This willleave only the unknown value on the left side ofthe equation:

50 g 10 mlX g100 ml

×=

6. Simplify the right side of the equation to solvefor X grams:

Answer: X g = 5 g

Example 2: You need to prepare a 500-mg chloram-phenicol dose in a syringe. The concentration ofchloramphenicol solution is 250 mg/ml. Howmany milliliters should you draw up into thesyringe?

1. Determine the known and unknown ratios.

1 mlKnown: 250 mg

mlUnknown: 500 mgX

2. Write the proportion.

ml 1 ml500 mg 250 mgX =

3. Cross multiply.

X ml × 250 mg = 1 ml × 500 mg

4. Divide.1 ml 500 mgX ml

250 mg×=

5. Simplify.

X ml = 2 ml

Answer: Draw up 2 ml in the syringe to preparea 500-mg dose of chloramphenicol.

Problem Set #6a. How many milligrams of magnesium sulfate are

in 10 ml of a 100 mg/ml magnesium sulfatesolution?

b. A potassium chloride (KCl) solution has aconcentration of 2 mEq/ml.

1.How many milliliters contain 22 mEq?

2.How many milliequivalents (mEq) in 15 ml?

c. Ampicillin is reconstituted to 250 mg/ml. Howmany milliliters are needed for a 1-g dose?


Concentration and Dilution

Terminology 5% dextrose in water is the same as D5W. 0.9% sodium chloride (NaCl) is the same as

normal saline (NS). Half-normal saline is half the strength of normal

saline (0.9% NaCl), or 0.45% NaCl. This mayalso be referred to as 0.5 NS or 1/2 NS.

Concentration Expressed as a PercentageThe concentration of one substance in another may beexpressed as a percentage or a ratio strength.

As stated earlier in this chapter, concentrationsexpressed as percentages are determined using one ofthe following formulas:

1. Percent weight-in-weight (w/w) is the grams of adrug in 100 grams of the product.

2. Percent weight-in-volume (w/v) is the grams of adrug in 100 ml of the product.

3. Percent volume-in-volume (v/v) is the millilitersof drug in 100 ml of the product.

Example 1:0.9% sodium chloride (w/v) = 0.9 g of sodiumchloride in 100 ml of solution.

Example 2:5% dextrose in water (w/v) = 5 g of dextrose in100 ml of solution.

Example 3:How many grams of dextrose are in 1 L of D5W?

Use the ratio and proportion method to solvethis problem:

Known ratio: D5W means 5 g

100 ml

Unknown ratio: 1LX g

1. Write the proportion:

51 L 100 mlX g g=

2. Are you ready to cross multiply? No. Remember,you must first convert the denominator of eitherterm so that both are the same. Because youknow that 1 L = 1000 ml, you can convert theunlike terms as follows:

51000 ml 100 mlX g g=

3. Now that the units are both placed in the sameorder and the units across from each other arethe same, you can cross multiply.X g × 100 ml = 5 g × 1000 ml

4. Divide:

5 1000 ml100 mlgXg ×=

5. Simplify:X g = 50 gAnswer: There are 50 g of dextrose in 1 L ofD5W.

Before you attempt problem sets #7 and #8, hereare a few suggestions for solving concentration anddilution problems:

1. First calculate the number of grams in 100 ml ofsolution. That is your “known” side of the ratio.

2. Then calculate the number of grams in thevolume requested in the problem by setting up aratio.

3. Check to make sure your units are in the sameorder in the ratio.

4. Make sure the units that are across from eachother in the ratio are the same.

5. After you have arrived at the answer, convertyour answer to the requested units.

Problem Set #7a. In 100 ml of a D5W/0.45% NaCl solution:

1. How many grams of NaCl are there?2. How many grams of dextrose are there?

b. How many grams of dextrose are in 1 L of a10% dextrose solution?

c. How many grams of NaCl are in 1 L of 1/2 NS?d. How many milligrams of neomycin are in 50 ml

of a 1% neomycin solution?e. How many grams of amino acids are in 250 ml

of a 10% amino acid solution?

Problem Set #8a. An order calls for 5 million units (MU) of

aqueous penicillin. How many milliliters areneeded if the concentration is 500,000 units/ml?

b. How many milliliters are needed for a 15-MUaqueous penicillin dose if the concentration ofthe solution is 1 MU/ml?

c. Pediatric chloramphenicol comes in a 100 mg/ml


concentration. How many milligrams are presentin 5 ml of the solution?

d. How many milliliters of a 250 mg/ml chloram-phenicol solution are needed for a 4-g dose?

e. Oxacillin comes in a 500 mg/1.5 ml solution.How many milliliters will be required for a 1.5-gdose?

f. How many grams of ampicillin are in 6 ml of a500 mg/1.5 ml solution?

g. How many milliliters contain 3 g of cephalothinif the concentration of the solution is 1 g/4.5 ml?

h. Use these concentrations to solve the following20 problems:Hydrocortisone 250 mg/2 mlTetracycline 250 mg/5 mlPotassium chloride (KCl) 2 mEq/mlAmoxicillin suspension 250 mg/5 mlMannitol 12.5 g/50 mlHeparin 10,000 units/mlHeparin 1000 units/ml 1. 10 mEq KCl = _____ml 2. 125 mg amoxicillin = _____ml 3. 750 mg hydrocortisone = _____ml 4. 1 g tetracycline = _____ml 5. 25 g mannitol = _____ml 6. 20,000 units heparin = _____ml OR

_____ml 7. 35 mEq KCl = _____ml 8. 6000 units heparin = _____ml OR _____ml 9. 40 mEq KCl = _____ml10. 600 mg hydrocortisone = _____ml11. _____mg hydrocortisone = 4 ml12. _____mg tetracycline = 15 ml13. _____mEq KCl = 15 ml14. _____g mannitol = 75 ml15. _____units or _____units heparin = 2 ml16. _____mEq KCl = 7 ml17. _____g tetracycline = 12.5 ml18. _____units or _____units heparin = 10 ml19. _____mEq KCl = 45 ml20. _____mg amoxicillin = 10 ml

i. How many grams of magnesium sulfate are in 2ml of a 50% magnesium sulfate solution?

j. How many grams of dextrose are in 750 ml of aD10W solution?

k. How many milliliters of a D5W solution contain7.5 grams of dextrose?

l. How many grams of NaCl are in 100 ml of a NSsolution?

m. How many grams of NaCl are in 100 ml of a 1/2NS solution?

n. How many grams of NaCl are in 100 ml of a 1/4NS solution?

o. How many grams of NaCl are in 1 L of a 0.45%NaCl solution?

p. How many grams of NaCl are in 1 L of a0.225% NaCl solution?

q. How many grams of dextrose are in 100 ml of aD5W/0.45% NaCl solution?

r. How many milliliters of a 70% dextrose solutionare needed to equal 100 g of dextrose?

s. How many milliliters of a 50% dextrose solutionare needed for a 10-g dextrose dose?

t. How many grams of dextrose are in a 50 ml NSsolution?

Concentration Expressed as a Ratio StrengthConcentration of weak solutions is frequently expressedas ratio strength.

Example: Epinephrine is available in three concen-trations: 1:1000 (read one to one thousand);1:10,000; and 1:200.A concentration of 1:1000 means there is 1 g ofepinephrine in 1000 ml of solution.

What does a 1:200 concentration of epinephrinemean?It means there is 1 g of epinephrine in 200 ml ofsolution.

What does a 1:10,000 concentration of epinephrinemean?It means there is 1 g of epinephrine in 10,000ml of solution.

Now you can use this definition of ratio strength toset up the ratios needed to solve problems.

Problem Set #9a. How many grams of potassium permanganate

should be used in preparing 500 ml of a 1:2500solution?


b. How many milligrams of mercury bichloride areneeded to make 200 ml of a 1:500 solution?

c. How many milligrams of atropine sulfate areneeded to compound the following prescription?

/RAtropine sulfate 1:200Dist. water qs ad 30 ml

d. How many milliliters of a 1:100 solution ofepinephrine will contain 300 mg of epinephrine?

e. How much cocaine is needed to compound thefollowing prescription?

/RCocaine 1:100Mineral oil qs ad 15 ml

f. How much zinc sulfate and boric acid areneeded to compound the following prescription?

/RZinc sulfate 1%Boric acid 2:100Distilled water qs ad 50 ml

Note: “qs ad” means “sufficient quantity to make.”

Dilutions Made from Stock SolutionsStock solutions are concentrated solutions used toprepare various dilutions. To prepare a solution of adesired concentration, you must calculate the quantityof stock solution that must be mixed with diluent toprepare the final product.

Calculating DilutionsExample 1: You have a 10% NaCl stock solutionavailable. You need to prepare 200 ml of a 0.5% NaClsolution. How many milliliters of the stock solution doyou need to make this preparation? How much morewater do you need to add to produce the final product?

1. How many grams of NaCl are in the requestedfinal product?

X g NaCl 0.5 g NaCl=200 ml soln 100 ml soln

Therefore, 200 ml of 0.5% NaCl solutioncontains 1 g of NaCl.

2. How many milliliters of the stock solution willcontain the amount calculated in step 1 (1 g)?

Remember, 10% means the solution contains 10g/100 ml.

X ml 100 ml = 1 g 10 gX ml = 10 ml

The first part of the answer is 10 ml of stocksolution.

3. How much water will you need to finish prepar-ing your solution?Keep in mind the following formula:(final volume) – (stock solution volume) =(volume of water)Therefore, for our problem,200 ml – 10 ml = 190 ml of waterThe second part of the answer is 190 ml ofwater.Example 2: You have to prepare 500 ml of a0.45% NaCl solution from a 10% NaCl stocksolution. How much stock solution and water doyou need?

1. How many grams of NaCl are in the requestedvolume? In other words, 500 ml of a 0.45%NaCl solution contains how much NaCl?

X g NaCl 0.45 g = 500 ml 100 ml

X g × 100 ml = 0.45 g × 500 ml0.45 g × 500 mlX g =

100 mlX g = 2.25 g

2. How many milliliters of stock solution willcontain the amount in step 1 (2.25 g)?

X ml × 10 g = 2.25 g × 100 mlX ml × 100 g = 2.25 g × 100 mlX ml = 2.25 g × 100 ml

10 gX ml = 22.5 ml

You will need 22.5 ml of stock solution.3. How much water will you need?

(Final volume) – (stock solution volume) =volume of water500 ml – 22.5 ml = 477.5 ml water


Answer: You will need 22.5 ml of stock solutionand 477.5 ml of water to make the final product.

Problem Set #10a. You need to prepare 1000 ml of a 1% neomycin

solution for a bladder irrigation. You have only a10% neomycin stock solution available in thepharmacy.1.How many milliliters of the stock solution doyou need to make this preparation?2.How many milliliters of sterile water do youneed to add to complete the product?

b. Sorbitol is available in a 70% stock solution. Youneed to prepare 140 ml of a 30% solution.1.How many milliliters of the stock solution areneeded to formulate this order?2.How much sterile water still needs to be addedto complete this product?

c. You need to make 1 L of dextrose solutioncontaining 35% dextrose.1.How many milliliters of the D70W do youuse?2.How much sterile water for injection still hasto be added?

d. You have a 10% amino acid solution. You needto make 500 ml of a 6% amino acid solution.1.How many milliliters of the stock solution areneeded to prepare this solution?2.How many milliliters of sterile water forinjection need to be added?

e. You receive the following prescription:

/RBoric acid 300 mgDist. water qs ad 15 ml1.How many milliliters of a 5% boric acidsolution are needed to prepare this prescription?2.How many milliliters of distilled water do youneed to add?

f. You need to prepare 180 ml of a 1:200 solutionof potassium permanganate (KMnO

4). A 5%

stock solution of KMnO4 is available.

1.How much stock solution is needed?2.How much water is needed?

g. How many milliliters of a 1:400 stock solutionshould be used to make 4 L of a 1:2000 solution?

h. You receive the following prescription:

/RAtropine sulfate 0.05%Dist. water qs ad 10 mlYou have a 1:50 stock solution of atropine sulfateavailable.1.How many milliliters of stock solution areneeded?2.How many milliliters of water are needed tocompound this prescription?

Dosage and Flow Rate CalculationsDosage Calculations

Basic Principles1. Always look for what is being asked:

Number of doses Total amount of drug Size of a dose

If you are given any two of the above, you can solve forthe third.

2. Number of doses, total amount of drug, andsize of dose are related in the following way:

Total amount of drugNumber of doses = Size of dose

This proportion can also be rearranged in thefollowing two ways:

Total amount of drug = (number of doses) × (sizeof dose)

ORTotal amount of drugSize of dose =

Number of doses

Calculating Number of Doses

Problem Set #11a. How many 10 mg doses are in 1 g?b. How many 5 ml doses can be made out of 2 fl oz?

Calculating Total Amount of Drug

Problem Set #12a. How many milliliters of ampicillin do you have

to dispense if the patient needs to take 2 tea-spoonfuls four times a day for 7 days?


Note: First, calculate the total number of dosesthe patient needs to receive; then, multiply thisnumber by the dose.

b. How many milligrams of theophylline does apatient receive per day if the prescriptionindicates 300 mg tid?

c. How many fluid ounces of antacid do you haveto dispense if the patient is to receive 1 TBS withmeals and at bedtime for 5 days?

Calculating Dose Size

Problem Set #13a. If a patient is to receive a total of 160 mg of

propranolol each day, and the patient takes onedose every 6 hours, how many milligrams are ineach dose?

b. If a daily diphenhydramine dose of 300 mg isdivided into six equal doses, how much do youhave to dispense for every dose?

Calculating the Correct DoseDosage calculations can be based on weight, bodysurface area, or age.

Calculating Dose Based on WeightDose (in mg) = [Dose per unit of weight (in mg/kg)] × [Weight of patient (in kg)]Dose/day (in mg/day) = [Dose/kg per day (inmg/kg per day)] × [Weight of patient (in kg)]

To find the size of each dose, divide the total doseper day by the number of doses per day as illustrated inthe following formula:

Total amount of drugSize of Dose = Number of doses

Problem Set #14a. A patient who weighs 50 kg receives 400 mg of

acyclovir q8h. The recommended dose is 5 mg/kg every 8 hours.1.Calculate the recommended dose for thispatient.2.Is the dose this patient is receiving greaterthan, less than, or equal to the recommendeddose?

b. The test dose of amphotericin is 0.1 mg/kg.What dose should be prepared for a patientweighing 220 lbs? (Remember, terms must be in

the same units before beginning calculations.)c. A 20-kg child receives erythromycin 25 mg q6h.

The stated dosage range is 30 to 100 mg/kg perday divided into four doses.1.What is the dosage range (in mg/day) this childshould receive?2.Is the dose this child is being given within thedosage range you have just calculated?

Calculating Dose Based on Body Surface AreaAs noted previously in this chapter, BSA is expressed asmeters squared (m2).

Problem Set #15a. An adult with a BSA of 1.5 m2 receives acyclovir.

The dose is 750 mg/m2 per day given in threeequal doses.1.Calculate the daily dose for this patient.2.Calculate the size of each dose for this patient.Note: These problems are done exactly like theweight problems; however, you should substitutemeters squared everywhere kilograms appearedbefore.

Calculating Dose Based on AgeThe following is an example of information that mightbe found on the label of an over-the-counter children’smedication:

St. Joseph’s Cough Syrup for ChildrenPediatric Antitussive Syrup

Active ingredient: Dextromethorphanhydrobromide 7.5 mg per 5 mlIndications: For relief of coughing associatedwith colds and flu for up to 8 hoursActions: AntitussiveWarnings: Should not be administered tochildren for persistent or chronic cough such asoccurs with asthma or emphysema, or whencough is accompanied by excessive secretions(except under physician’s advice)How supplied: Cherry-flavored syrup in plasticbottles of 2 and 4 fl ozDosage: (see table below)

Age Weight DosageUnder 2 yr below 27 lb As directed by

physician

2 to under 6 yr 27 to 45 lb 1 tsp every 6 to 8 h (not


to exceed 4 tsp daily)

6 to under 12 yr 46 to 83 lb 2 tsp every 6 to 8 h (notto exceed 8 tsp daily)

12 yr and older 84 lb and 4 tsp every 6 to 8 hgreater (not to exceed 16 tsp daily)

Problem Set #16a. Based on the preceding dosing table:

1.What is the dose of St. Joseph’s for a 5-year-old child?2.What should you dispense for a 12-year-oldchild weighing 30 kg?

b. The usual dose of ampicillin is 100 mg/kg perday. The prescription for a 38-kg child is writtenas 1 g q6h.1.Is this dose acceptable?2.If not, what should it be?

c. Propranolol is given as 0.5 mg/kg per day,divided every 6 h.1.What should a 10-kg child receive per day?2.What is the size of every dose?

d. Aminophylline is given at a rate of 0.6 mg/kg perhr.1.What daily dose will a 50-kg patient receive?2.If an oral dose is given every 12 h, what will itbe?

IV Flow Rate CalculationsUsing flow rates, you can calculate the volume of fluidor the amount of drug a patient will be receiving over acertain period of time. Prefilled IV bags are available ina number of volumes including: 50, 100, 250, 500, and1000 ml.

Calculating Volume of FluidDaily volume of fluid (in ml/day) =[Flow rate (in ml/h)] × [24 h/day]

Problem Set #17a. D5W is running at 40 ml/hr.

1.How many milliliters of D5W does the patientreceive per day?2.Which size D5W container will you dispense?

b. D5W/NS is prescribed to run at 100 ml/h.1.How much IV fluid is needed in 24 h?2.How will you dispense this volume?

c. A patient has two IVs running: D5W/0.5NS at10 ml/h and a hyperalimentation solution at 70ml/h. How much fluid is the patient receivingper day from these IVs?

Calculating Amount of Drug

Problem Set #18a. An order is written as follows: 1 g of aminophyl-

line in 1 L D5W/0.225% NaCl to run at 50 ml/h. How much aminophylline is the patientreceiving per day?

b. The dose of aminophylline in a child is 1 mg/kgper hour.1.If the child weighs 40 kg, at what rate shouldthe IV in question “a” be running?2.What should the daily dose be?

c. You add 2 g of aminophylline to 1 L of D5W. Ifthis solution is to run at 10 ml/h, how muchdrug will the patient receive per day?

d. If the dose of aminophylline should be 0.6 mg/kgper hour and the patient weighs 40 kg, at whatrate should the IV in question “c” be running?

Calculation of IV Flow (Drip) RatesCalculation of IV flow (drip) rates is necessary toensure that patients are getting the amount of medica-tion the physician ordered. For example, if an order iswritten as 25,000 units of heparin in 250 ml D5W toinfuse at 1000 units/h, what is the correct rate ofinfusion (in ml/h)?

Total amount of drugConcentration of IV = Total volume

25,000 units heparinConcentration of IV = 250 ml D5W

Concentration of IV = 100 units/ml of D5W

Now that you have calculated the concentration permilliliter, you can determine exactly what the rateshould be by using the following formula:

Dose desiredIV Rate = Concentration of IV(1,000 units/h)IV Rate = (100 units/ml)

IV Rate = 10 ml/h

Problem Set #19a. An order is written for 2 g of lidocaine in 250 ml

of D5W to infuse at 120 mg/h. What is the


correct rate of infusion (in ml/h)?b. An order is written for 25,000 units of heparin

in 250 ml of D5W. The doctor writes to infuse17 ml/h. How many units of heparin will thepatient receive in a 12-hour period?

Moles, Equivalents, Osmolarity,Isotonicity, and pH

Moles and EquivalentsA mole is one way of expressing an amount of achemical substance or a drug.

Examples: A mole of NaCl (sodium chloride) weighs58.45 g.A mole of KCl (potassium chloride) weighs 74.55 g.

An equivalent usually expresses the amount ofeach part (or element) of a chemical substance ora drug.

Examples: One mole of NaCl contains one equiva-lent of Na+ (which weighs 23 g).One mole of NaCl also contains one equivalentof Cl- (which weighs 35.45 g).

Remember, 1 equivalent (Eq) =1000 milliequivalents (mEq).

Numbers to RememberIf you forget these numbers, these equivalents can befound on the labels of the large-volume sodium anddextrose solutions.

a. 0.9% NaCl contains 0.9 g NaCl in every 100 mlof solution,

or0.9% NaCl contains 9 g NaCl in every liter ofsolution.

b. 0.9% NaCl contains 15.4 mEq Na+ in every 100ml of solution,

or

0.9% NaCl contains 154 mEq Na+ in every literof solution.

c. 0.45% NaCl (1/2 NS) contains 0.45 g NaCl inevery 100 ml of solution, or 7.7 mEq of Na+ inevery 100 ml of solution,

or0.45% NaCl contains 4.5 g NaCl in every literof solution, or 77 mEq of Na+ in every liter ofsolution.

d. The table below summarizes some of the data.grams of grams of milliequivalents ofNaCl/100 ml NaCl/liter Na+/liter

0.9% NaCl (NS) 0.9 9 1540.45% NaCl (1/2 NS) 0.45 4.5 770.225% NaCl (1/4 NS) 0.225 2.25 38.5

Problem Set #20a. You need to make 1 L of NS. You have 1 L of

SWI (Sterile Water for Injection) and a vial ofNaCl (4 mEq/ml). How will you prepare thissolution?

b. An order calls for D10W/0.45% NaCl to run at40 ml/h. You have 1 L of D10W and a vial ofNaCl (4 mEq/ml) available. How would youprepare this bottle?

c. How would you prepare 500 ml of a D10W/0.225% NaCl solution if you have SWI, NaCl (4mEq/ml), and a 50% dextrose solution available?

d. You have D10W and a vial of NaCl (4 mEq/ml).How would you prepare 250 ml of a D10W/NSsolution?

Osmolarity and IsotonicityOsmolarity expresses the number of particles (osmols)in a certain volume of fluid.

Remember, 1 osmol (Osm) = 1000 milliosmols(mOsm).

The osmolarity of human plasma is about 280 to300 mOsm/L.

The osmolarity of NS is about 300 mOsm/L, andthe osmolarity of D5W is about 280 mOsm/L.

Solutions of the same osmolarity are called iso-tonic.

Example: NS and plasma are isotonic.If parenteral fluids are administered that are notisotonic, the result could be irritation of veinsand swelling or shrinking of red blood cells.Solutions having osmolarities higher than that ofplasma are known as hypertonic solutions.

Examples: Hyperalimentation solutions and D5W/NS are hypertonic.Solutions having osmolarities lower than that ofplasma are called hypotonic solutions.

Example: 1/2 NS is hypotonic.

pHpH refers to the acidity or basicity of a solution.


The pH scale ranges from 1 to 14.pH = 7 is neutralpH < 7 is acidicpH > 7 is basicNormal human plasma has a pH of approxi-mately 7.4.

Parenteral solutions with pHs different from that ofnormal human plasma can be very irritating to tissuewhen injected. Examples are phenytoin and diazepam.Ophthalmologic preparations are buffered to maintaina pH as close to 7.4 as possible.

Some drugs are not stable at a certain pH. Oneexample is ampicillin, which is not very stable in acidicsolutions. D5W solutions are slightly acidic, whereasNS solutions are more neutral. Therefore, ampicillininjection is dispensed in NS rather than D5W.

StatisticsThe arithmetic mean is a value that is calculated bydividing the sum of a set of numbers by the totalnumber of number sets. This value is also referred to asan average. The following formula is used to determinethe average:

M = ∑X Nwhere ∑= sumM = mean (average)X = one value in set of dataN = number of values X in data set

Now, using the formula, follow these two steps tocalculate the arithmetic mean age of five pharmacistswhose ages are 25, 28, 33, 47, and 54 years.

1. Find the sum of all ages.2. Divide the sum by total number of pharma-cists:25 + 28 + 33 + 47 + 54 = 187 = 37.4 years

5 5The median is a value in an ordered set of values

below and above which there are an equal number ofvalues. When an even number of measurements arearranged according to size, the median is defined as themean of the values of the two measurements that arenearest to the middle.

Example 1: Determine the median temperature fora medication refrigerator whose temperature

reading was 37°F, 39°F, 40°F, 44°F, and 38°F on5 consecutive days.

1. Arrange the temperature readings according tosize, smallest to largest.37° 38° 39° 40° 44°

2. The median is 39°.Example 2: Determine the median temperature for

a medication refrigerator whose temperaturereading was 45°F, 40°F, 43°F, 39°F, 46°F, and40°F on 6 consecutive days.

1. Arrange the temperature readings according tosize, smallest to largest.39° 40° 40° 43° 45° 46°

2. The median is 40 + 43 = 83 = 41.5 2 2

Standard deviation is a statistic that tells you howtightly clustered the data points are around the mean ina set of data. Standard deviation can be calculated byusing the following formula:

Ω = √ ∑(X-M)2 × 1/(N-1)Where Ω = standard deviationX = one value in set of dataM = the mean of all values X in your set of dataN = the number of values X in your set of dataGraphically, when the individual values are

bunched around the mean in a set of data, the bell-shaped curve is steep. Conversely, when the individualvalues are widely spread around the mean in a set ofdata, the bell-shaped curve is flat (see Figure 5-1).

One standard deviation away from the mean ineither direction on the X axis accounts for about 68%of the individual values in the data set. Two standarddeviations away from the mean in either direction onthe X axis accounts for about 95% of the individualvalues in the data set. Three standard deviations awayfrom the mean in either direction on the X axisaccounts for about 99% of the individual values in the

Figure 5-1. Bell Curve


data set. If the curve were flatter and more spread out,the standard deviation would be larger to account for68% of the individual values in the data set. Thestandard deviation can help you explain data andevaluate various studies.

Example: Using the following steps, calculate thestandard deviation for body weight of normalmales according to the table below:

Normal Males Body Weight (pounds)

1 154

2 175

3 162

4 213

5 191

6 187

7 158

8 202

9 185

10 230

1. Calculate the mean (average) of all body weightsby adding all body weights and dividing by thetotal number of normal males.X = ∑X N∑X = 154 + 175 + 162 + 213 + 191 + 187 +158 + 202 + 185 + 230 = 1,857 poundsN = 10X = 1,857 pounds = 185.7 pounds 10

2. For each of the individual male body weights,subtract the mean (average) body weight fromthe individual male body weights, then multiplythat value by itself (also known as determiningthe square).(154 – 185.7)2 = 1004.89(175 – 185.7)2 = 114.49(162 – 185.7)2 = 561.69(213 – 185.7)2 = 745.29(191 – 185.7)2 = 28.09(187 – 185.7)2 = 1.69(158 – 185.7)2 = 767.29(202 – 185.7)2 = 265.69(185 – 185.7)2 = 0.49(230 – 185.7)2 = 1962.49

3. Sum up all the squared values.1004.89 + 114.49 + 561.69 + 745.29 + 28.09 +1.69 + 767.29 + 265.69 + .49 + 1962.49 =5452.1

4. Multiply the sum of all the squared values by 1/(N-1) and take the square root of the resultingvalue to obtain the standard deviation for malebody weights.(5452.1) × (1/(N-1)) =(5452.1) × (1/(10-1)) = 605.79√605.79 = 24.61

Ideal Body Weight (IBW)You need to know a patient’s IBW to determine theestimated creatinine clearance of an individual patient.The estimated creatinine clearance is needed todetermine the appropriate dose of renally excretedmedications, such as tobramycin. The followingformula is used for calculating the IBW for a male:

IBW male (kg) = 50 + (2.3 × height in inches) 5 feet

The following formula is used for calculating theIBW for a female:

IBW female (kg) = 45.5 + (2.3 × height in inches) 5 feet

Example: Calculate the IBW for a male who is 6 feet2 inches tall.

1. Convert the height to inches.6 feet x 12 inches/foot = 72 inches + 2 inches =74 inches

2. Using the formula for calculating the IBW for amale, multiply 2.3 times 74 inches.2.3 × 74 = 170.2

3. Divide 170.2 by 5 feet.170.2 inches/5 feet = 34.04

4. Add 50 to 34.04 to obtain the ideal body weight.50 + 34.04 = 84.04 kg

Practice Calculations 1 1. What does ss mean?_____ 2. Write II as an Arabic numeral:_____ 3. Write 2/5 as a decimal fraction:_____ 4. The fraction form of 0.1 is:_____ 5. Express 25% as a fraction:_____


6. Write 0.88 as a percentage:_____ 7. Express 1/4 as a percentage:_____ 8. The fraction form of 0.4 is:_____ 9. Express xiv in Arabic numerals:_____10. Write 1 1/2 in decimal form:_____11. The standard metric system measure for weight

is the:_____12. The standard metric system measure for length

is the:_____13. The standard metric system measure for volume

is the:_____14. 1 km = _____ m15. 1 L = _____ ml16. 1 kg = _____ g17. 1 g = _____ mg18. 1 mg = _____ g19. 0.01 g = _____ mg20. 1 ml = _____ L21. 1 tsp = _____ TBS22. 1 cup = _____ ml23. 1 TBS = _____ fl oz24. 15 ml = _____ TBS25. 1 cup = _____ fl oz26. 1000 ml = _____ L27. 2 kg = _____ g28. 1 gal = _____ qt29. 1 pt = _____ cups30. 1 mm = _____ m31. 1 tsp = _____ ml32. 5 gr = _____ g33. 3 cups = _____ ml34. 70 kg = _____ lb35. 45 ml = _____ fl oz36. 80 mg = _____ gr37. 250 mg = _____ g38. 3 TBS = _____ tsp39. 2 fl oz = _____ TBS40. 3 qt = _____ pt41. 120 ml = _____ cups42. 10 ml = _____ tsp43. 45 ml = _____ TBS

44. 50 mg = _____ mg45. 2 gal = _____ qt46. 0.5 pt = _____ ml47. 20 kg = _____ lb48. 750 mg = _____ g49. 25 ml = _____ tsp50. 6 tsp = _____ TBS

Practice Calculations 2 1. 6% (w/w) = _____

10% (w/v) = _____0.5% (v/v) = _____

2. A patient needs a 300-mg dose of amikacin.How many milliliters do you need to draw froma vial containing 100 mg/2 ml of amikacin?

3. A suspension of naladixic acid contains 250 mg/5 ml. The syringe contains 15 ml. What is thedose (in milligrams) contained in the syringe?

4. How many milligrams of neomycin are in 200ml of a 1% neomycin solution?

5. 1/2 NS = _____ g NaCl / _____ ml solution 6. How many grams of pumpkin are in 300 ml of a

30% pumpkin juice suspension? 7. Express 4% hydrocortisone cream as a ratio.

(Remember that solids, such as creams, areusually expressed as weight-in-weight.)

8. You have a solution labeled D10W/NS.a) How many grams of NaCl are in 50 ml of thissolution?b)How many milliliters of this solution contain50 g dextrose?

9. A syringe is labeled “inamrinone 5 mg/ml, 20ml.” How many milligrams of inamrinone are inthe syringe?

10.Boric acid 2:100 is written on a prescription.This is the same as _____ boric acid in _____solution.

11.How much epinephrine do you need to prepare20 ml of a 1:400 epinephrine solution?

12.Calculate the amounts of boric acid and zincsulfate to fill the following prescription:

/RZinc sulfate 0.5%Boric acid 1:50


Distilled water qs. ad 100 ml13.Use the following concentrations to solve the

problems:Gentamicin 80 mg/mlMagnesium sulfate 50%Atropine 1:200a) 120 mg gentamicin = _____ mlb)100 mg atropine = _____ mlc) _____ g magnesium sulfate = 150 ml

Practice Calculations 31. You need to prepare 1 L of 0.25% acetic acid

irrigation solution. The stock concentration ofacetic acid is 25%.a. How many milliliters of stock solution do youneed to use?b.How many milliliters of sterile water do youneed to add?

2. A drug order requires 500 ml of a 2% neomycinsolution.a. How much neomycin concentrate (1 g/2 ml)do you need to fill the order?b.How many milliliters of sterile water must youadd to the concentrate before dispensing thedrug?

3. a. Calculate the amount of atropine stocksolution (concentration 0.5%) needed to com-pound the following prescription:

/RAtropine sulfate 1:1500Sterile water qs ad 300 mlb.How much sterile water do you have to add tocomplete the order?

4. How many tablets do you have to dispense forthe following prescription?

/RObecalp ii tablets tid for 10 days

5. How many 2 tsp doses can a patient take from abottle containing 3 fl oz?

6. A patient is receiving a total daily dose of 2 g ofacyclovir. How many milligrams of acyclovir ishe receiving per dose if he takes the drug fivetimes a day?

7. The recommended dose of erythromycin to treat

an ear infection is 50 mg/kg per day given q6h.Answer the following questions regarding thisdrug:a. If a child weighs 20 kg, how much erythromy-cin should he receive per day?b.How much drug will he receive per dose?

8. The dose of prednisone for replacement therapyis 2 mg/m2 per dose. The drug is administeredtwice daily. What is the daily prednisone dose fora 1.5-m2 person?

9. An aminophylline drip is running at 1 mg/kg perhour in a 10-kg child. How much aminophyllineis the child receiving per day?

10. A child with an opiate overdose needs naloxone.The recommended starting dose is 0.1 mg/kg.The doctor writes for 0.3 mg naloxone stat.Answer the following questions on the basis ofthe child’s weight of 26.4 lbs.:a. What is the child’s weight in kg?b.On the basis of the answer to “a,” does 0.3 mgsound like a reasonable dose?

11. An IV fluid containing NS is running at 80 ml/h.a. How much fluid is the patient receiving perday?b.How many 1-L bags will be needed per day?

12. A patient has two IVs running: an aminophyllinedrip at 20 ml/h and saline at 30 ml/h. Howmuch fluid is the patient receiving per day fromthe IVs?

13. a. You prepare a solution by adding 2 g ofBronkospaz to 1 L of NS. What is the concentra-tion of Bronkospaz?b.If the solution of Bronkospaz you made in “a”runs at 30 ml/h, how much Bronkospaz is thepatient receiving per day?c. If a 60-kg patient should receive 1 mg/kg perhour, will the dose in “b” be appropriate?

Answers to Problems SetsProblem Set #1:a. 2 b. 605 c. 20 d. 3e. 7 f. 4 g. 9 h. 15i. 11 j. 1030 k. 14 l. 16

Problem Set #2:a. 0.5 b. 0.75 c. 1 d. 0.4


e. 667/1000 f. 0.625 g. 0.5 h. 0.25i. 5.5 j. 2.67 k. 5.25 l. 3.8m. 1/4 n. 2/5 o. 3/4 p. 7/20q. 2 1/2 r. 1 3/5 s. 3 1/4 t. 1/3

Problem Set #3:a. 23/100 b. 67/100 c. 1/8 d. 1/2e. 66.7/100 f. 3/4 g. 33/50 h. 2/5i. 1 j. 3/20 k. 50% l. 25%m. 40% n. 24% o. 4% p. 50%q. 35% r. 44% s. 57% t. 99%

Problem Set #4:a. 1000 mlb. 1 kgc. 1000 mgd. 1 mge. 3 tspf. 15 mlg. 1 cuph. 240 mli. 1 TBSj. 5 mlk. 16 TBSl. 480 mlm. 2 TBSn. 2 pt

Problem Set #5:a. 1 fl ozb. 0.5 gc. 0.5 fl ozd. 4 tspe. 3500 gf. 0.00025 gg. 1.5 Lh. 6 gali. 390 mgj. 54.5 kgk. 90 mll. 158.4 lbm. 1.97 pt

n. 1.76 lbo. 15 mlp. 1 fl ozq. 30 mlr. 20 fl ozs. 32.5 mgt. 500 mlu. 5 grv. 4 TBSw. 2 fl ozx. 65.5 kgy. 6 tspz. 20 mlaa. 28.3°Cbb. –22.2°Ccc. 41°Fdd. 89.6°Fee. 2.1 m2

Problem Set #6:a. 1000 mgb. 1. 11 ml

2. 30 mEqc. 4 ml

Problem Set #7:a. 1. 0.45 g

2. 5 gb. 100 gc. 4.5 gd. 500 mge. 25 g

Problem Set #8:a. 10 mlb. 15 mlc. 500 mgd. 16 mle. 4.5 mlf. 2 gg. 13.5 mlh. 1. 5 ml


2. 2.5 ml 3. 6 ml 4. 20 ml 5. 100 ml 6. a. 2 ml of heparin 10,000 units/ml or b. 20 ml of heparin 1000 units/ml 7. 17.5 ml 8. a. 0.6 ml of heparin 10,000 units/ml or b. 6 ml of heparin 1000 units/ml 9. 20 ml10. 4.8 ml11. 500 mg12. 750 mg13. 30 mEq14. 18.75 g15. 20,000 units or 2000 units16. 14 mEq17. 0.625 g18. 100,000 units or 10,000 units19. 90 mEq20. 500 mg

i. 1 gj. 75 gk. 150 mll. 0.9 gm. 0.45 gn. 0.225 go. 4.5 gp. 2.25 gq. 5 gr. 142.9 mls. 20 mlt. 0

Problem Set #9:a. 0.2 gb. 400 mgc. 150 mgd. 30 mle. 150 mg

f. 500 mg of zinc sulfate and 1 g of boric acid

Problem Set #10:a. 1. 100 ml of stock solution

2. 900 ml of waterb. 1. 60 ml of stock solution

2. 80 ml of waterc. 1. 500 ml of D70W

2. 500 ml of sterile waterd. 1. 300 ml of stock solution

2. 200 ml of sterile watere. 1. 6 ml of 5% boric acid

2. 9 ml of distilled waterf. 1. 18 ml of stock solution

2. 162 ml of waterg. 800 ml of stock solutionh. 1. 0.25 ml of stock solution

2. 9.75 ml of water

Problem Set #11:a. 100 dosesb. 12 doses

Problem Set #12:a. 280 ml of ampicillinb. 900 mg of theophyllinec. 10 fl oz

Problem Set #13:a. 40 mg of propranololb. 50 mg for every dose

Problem Set #14:a. 1. 250 mg q8h

2. greater than the recommended doseb. 10 mgc. 1. 600–2000 mg/day

2. no

Problem Set #15:a. 1. 1125 mg

2. 375 mg

Problem Set #16:a. 1. 1 tsp every 6 to 8 h not to exceed 4 tsp daily


2. 2 tsp every 6 to 8 h not to exceed 8 tsp daily(Defer to weight when there is a difference between theweight-based dose and the age-based dose, since weightis a more accurate basis for dosing medications ingeneral.)b. 1. no (Depending on your facility’s roundingconventions, this dose may be considered correct.) 2. 3800 mg/dayc. 1. 5 mg/day 2. 1.25 mg per dosed. 1. 720 mg 2. 360 mg every 12 hours

Problem Set #17:a. 1. 960 ml 2. 1000 mlb. 1. 2400 ml 2. 3000 ml, three 1-L bagsc. 1920 ml of fluid

Problem Set #18:a. 1.2 gb. 1. 40 ml/h 2. 960 mg/dayc. 480 mg/dayd. 12 ml/hr

Problem Set #19:a. 15 ml/hb. 20,400 units

Problem Set #20:a. Add 38.5 ml NaCl to 1 L SWFIb. Add 19.25 ml NaCl to 1 L D10Wc. 4.81 ml NaCl plus 100 ml D50W; qs with SWFI to500 mld. 9.625 ml NaCl; qs with D10W to 250 ml

Answers to Practice Calculations 1 1. 1/2 2. 2 3. 0.4 4. 1/10 5. 1/4 6. 88%

7. 25% 8. 2/5 9. 1410. 1.511. gram12. meter13. liter14. 100015. 100016. 100017. 100018. 0.00119. 1020. 0.00121. 1/322. 24023. 0.524. 125. 826. 127. 200028. 429. 230. 0.00131. 532. 0.32533. 72034. 15435. 1.536. 1.2337. 0.2538. 939. 440. 641. 0.542. 243. 344. 0.0545. 846. 240


47. 4448. 0.7549. 550. 2

Answers to Practice Calculations 2 1. 6 g/100 g

10 g/100 ml0.5 ml/100 ml

2. 6 ml 3. 750 mg 4. 2000 mg 5. 0.45 g/100 ml 6. 90 g 7. 4 g/100 g 8. a. 0.45 g

b. 500 ml 9. 100 mg10. 2 g in 100 ml11. 0.05 g or 50 mg12. 0.5 g zinc sulfate and 2 g boric acid13. a. 1.5 ml

b. 20 mlc. 75 g

Answers to Practice Calculations 31. a. 2.5 g acetic acid = 10 ml stock solution

b. 990 ml sterile water2. a. 10 g neomycin = 20 ml stock solution

b. 480 ml sterile water3. a. 0.2 g atropine sulfate = 40 ml stock solution

b. 260 ml sterile water4. 60 tablets5. 9 doses6. 400 mg per dose7. a. 1000 mg per day

b. 250 mg per dose8. 6 mg per day9. 240 mg per day10. a. 12 kg

b. No, the calculated dose is 1.2 mg.11. a. 1920 ml per day

b. 2 1-L bags per day12. 1200 ml per day13. a. 2000 mg/1000 ml or 2 mg/ml or

2 g/1000 ml or 2 g/L or 2:1000b. 1440 mg/dayc. Yes, dose is appropriate.


APPENDIX 5-1

Table 1

micro-(mc): 1/1,000,000 = 0.000001milli-(m): 1/1000 = 0.001centi-(c): 1/100 = 0.01deci-(d): 1/10 = 0.1

Table 2

deca-(da) : 10hecto-(h): 100kilo-(k): 1000mega-(M): 1,000,000

Table 3

1 kilometer (km) = 1000 meters (m)

0.001 kilometer (km) = 1 meter (m)

1 millimeter (mm) = 0.001 meter (m)

1000 millimeters (mm) = 1 meter (m)

1 centimeter (cm) = 0.01 meter (m)

100 centimeters (cm) = 1 meter (m)

Table 4

1 milliliter (ml) = 0.001 liter (L)

1000 milliliters (ml) = 1 liter (L)

1 microliter (mcl) = 0.000001 liter (L)1,000,000 microliters (mcl) = 1 liter (L)

1 deciliter (dl) = 0.1 liter (L)

10 deciliters (dl) = 1 liter (L)

Table 5

1 kilogram (kg) = 1000 grams (g)

0.001 kilogram (kg) = 1 gram (g)

1 milligram (mg) = 0.001 gram (g)

1000 milligrams (mg) = 1 gram (g)

1 microgram (mcg) = 0.000001 gram (g)

1,000,000 micrograms (mcg) = 1 gram (g)

Table 6

Pound Ounces Drams Scruples Grains

1 = 12 = 96 = 288 = 5760

1 = 8 = 24 = 480

1 = 3 = 60

1 = 20

Table 7

Gallon Pints Fluid ounces Fluid drams Minims1 = 8 = 128 = 1024 = 61,440

1 = 16 = 128 = 7,680

1 = 8 = 480

1 = 60

Table 8

Pound Ounces Grains(lb) (oz) (gr)

1 = 16 = 7000

1 = 437.5

Table 9

1 meter (m) = 39.37 (39.4) inches (in)1 inch (in) = 2.54 centimeters (cm)1 micron (mc) = 0.000001 meter (m)

Table 10

1 milliliter (ml) = 16.23 minims (m.)

1 fluid ounce (fl oz) = 29.57 (30) milliliters (ml)

1 liter (L) = 33.8 fluid ounces (fl oz)

1 pint (pt) = 473.167 (480) milliliters (ml)

1 gallon (gal) = 3785.332 (3785) milliliters (ml)

Table 11

1 kilogram (kg) = 2.2 pounds (lb)

1 pound avoir (lb) = 453.59 (454) grams (g)

1 ounce avoir (oz) = 28.35 (28) grams (g)

1 ounce apoth (oz) = 31.1 (31) grams (g)

1 gram (g) = 15.432 (15) grains (gr)


1 grain (gr) = 65 milligrams (mg)

1 ounce (avoir) (oz) = 437.5 grains (gr)

1 ounce (apoth) = 480 grains (gr)

Table 12 milliequiva-

grams of grams of lents ofNaCl/100 ml NaCl/liter Na+/liter

0.9% NaCl (NS) 0.9 9 154.5

0.45% NaCl (1/2 NS) 0.45 4.5 77

0.225% NaCl (1/4 NS) 0.225 2.25 38.5

FootnotesThis chapter was adapted with permission from the JohnsHopkins Hospital Technician Training Course 1991: 106–38.

pharmacy calculations

Documents

estimated

body surface

smaller roman

dividends

ideal body

larger roman

calculating

stock solution