Pharmaceutical Calculations 15th Edition PDF

https://t.me/MedicalBooksStore Pharmaceutical Calculations 15 h Edit ion Pharmaceutical Calculations 15 h Edit ion H war C. A sel, Phd Professor and Dean Emeritus College of Pharmacy...

https://t.me/MedicalBooksStore Pharmaceutical Calculations 15 h Edit ion Pharmaceutical Calculations 15 h Edit ion H war C. A sel, Phd Professor and Dean Emeritus College of Pharmacy University of Georgia Athens, Georgia Shelly J. S ck , Phd, RPh Professor College of Pharmacy Southwestern Oklahoma State University Weatherford, Oklahoma Senior Acquisitions Editor: Tari Broderick Product Development Editor: Stephanie Roulias Production Project M anager: Priscilla Crater Designer: H olly McLaughlin M anufacturing Coordinator: Margie O rzech M arketing M anager: Lisa Zoks Prepress Vendor: SPi G lobal 15th Edition Copyright © 2017 Wolters Kluwer Copyright © 2013 Wolters Kluwer H ealth | Lippincott W illiams & W ilkins. Copyright © 2010, 2006, 2001, 1996, 1991, 1986 by Lippincott W illiams & W ilkins. All rights reserved. T his book is protected by copyright. N o part of this book may be reproduced or transmitted in any form or by any means, including as photocopies or scanned-in or other electronic copies, or utilized by any information storage and retrieval system without writ- ten permission from the copyright owner, except for brief quotations embodied in critical articles and reviews. Materials appearing in this book prepared by individuals as part of their official duties as U.S. government employ- ees are not covered by the above-mentioned copyright. To request permission, please contact Wolters Kluwer at Two Commerce Square, 2001 Market Street, Philadelphia, PA 19103, via email at [email protected], or via our website at lww.com (products and services). 9 8 7 6 5 4 3 2 1 Printed in China Library of Congress Cataloging-in-Publication D ata N ames: Ansel, H oward C., 1933- , author. | Stockton, Shelly J., author. T itle: Pharmaceutical calculations / H oward C. Ansel, Shelly J. Stockton. D escription: 15th edition. | Philadelphia : Wolters Kluwer, | Includes bibliographical references and index. Identifiers: LCCN 2015039620 | ISBN 9781496300713 (alk. paper) Subjects: | MESH : D rug D osage Calculations. | Pharmaceutical Preparations—administration & dosage. Classification: LCC RS57 | N LM Q V 748 | D D C 615.1/401513—dc23 LC record available at http://lccn.loc. gov/2015039620 T his work is provided “as is,” and the publisher disclaims any and all warranties, express or implied, including any warranties as to accuracy, comprehensiveness, or currency of the content of this work. T his work is no substitute for individual patient assessment based upon healthcare professionals’ examination of each patient and consideration of, among other things, age, weight, gender, current or prior medical conditions, medication history, laboratory data and other factors unique to the patient. T he publisher does not provide medi- cal advice or guidance and this work is merely a reference tool. H ealthcare professionals, and not the publisher, are solely responsible for the use of this work including all medical judgments and for any resulting diagnosis and treatments. G iven continuous, rapid advances in medical science and health information, independent professional verifica- tion of medical diagnoses, indications, appropriate pharmaceutical selections and dosages, and treatment options should be made and healthcare professionals should consult a variety of sources. W hen prescribing medication, healthcare professionals are advised to consult the product information sheet (the manufacturer’s package insert) accompanying each drug to verify, among other things, conditions of use, warnings and side effects and identify any changes in dosage schedule or contraindications, particularly if the medication to be administered is new, infrequently used or has a narrow therapeutic range. To the maximum extent permitted under applicable law, no responsibility is assumed by the publisher for any injury and/or damage to persons or property, as a matter of products liability, negligence law or otherwise, or from any reference to or use by any person of this work. LW W.com  Preface T he 15th edition of Pharmaceutical Calculations marks the introduction of Professor Shelly Stockton as co-author. Professor Stockton’s experience in pharmacy practice and her exper- tise in teaching pharmaceutics and pharmacy calculations are reflected in her substantial contributions to this textbook. Combined with the many progressive changes recom- mended by a select review team of pharmacy students, practitioners, and educators, this new edition maintains the standard for today’s academic and basic practice requirements in the subject area of pharmaceutical calculations. Each chapter has been thoroughly revised with the focus directed toward providing basic pharmaceutical calculations along with supporting explanations of the pharmaceutical or clinical purpose underpinning each type of calculation. H undreds of new problems have been added to include many current products encountered in pharmacy practice. Relevance is further demonstrated by the inclusion of select product labels directly linked to example problems. N ew in this edition are Authors’ Extra Points that provide brief explanations of select underlying subjects, as: pharmacopeias, electronic prescriptions, drug names, and the regu- lation of pharmacy compounding. A section on equianalgesic dosing for narcotic analgesics has been added to Chapter 10 along with dosing tables related to the subject. All of the valued features of the previous edition have been retained and enhanced, including the following: in-chapter example problems with step-by-step solutions; end-of- chapter practice problems with answers; Case-in-Point features that provide clinical or phar- maceutical case studies; Calculations Capsules that provide boxed summaries of chapter calculations; CalcQuiz sections that provide a limited number of unsolved problems, useful as homework, quiz, or assessment exercises; and, the Comprehensive Review Problems at the end of the book that provide multipart solved problems for student use as a final self-assessment. T hroughout its history, this textbook has served as a valuable resource in meeting the instructional needs of pharmacy students in the area of pharmaceutical calculations. T his new edition is expected to continue to meet that need. Compan on Web s te Pharmaceutical Calculations, 15th edition, includes additional resources for both instructors and students, available on the book’s companion Web site at http://thePoint.lww.com/Ansel15e. Resources for Students Interactive math calculations Q uiz Bank, with more than 400 review problems and detailed solutions Resources for instructors CalcQ uiz Solutions Searchable Full Text O nline See the inside front cover for more details, including the passcode you will need to gain access to the Web site. v  Acknowledgments T he author gratefully acknowledges the contributions to this revision by the following per- sons: Tom Schoenbachler, for insights into contemporary community pharmacy practice; D eborah Elder, for contributions in the area of pharmacy compounding; Ken D uke, for problems in the area of nuclear pharmacy; Warren Beach, for some Case-in-Point calcula- tions; Flynn Warren, for a host of problems including many relating to institutional phar- macy practice; Michael Ansel and Catherine Chuter, for information on the verification and data processing of electronic prescriptions; Les Ramos and Margaret Ramos, for their input in various areas of clinical calculations; H ardeep Saluja and Sarai Flynn for contributions to the chapter on bioavailability and pharmacokinetics; Patra Kositchaiwat and Ryan Varghese for their input in the area of electrolyte solution calculations; and Loyd V. Allen, Jr. for his continued courtesy in allowing use of formulas published in the International Journal of Pharmaceutical Compounding. G ratitude is expressed to the following reviewers, whose experience was drawn upon during the planning process and whose thoughtful analysis and constructive comments led to many of the changes in this revision: Stacy Cairns, Kimberly D augherty, D avid D ubins, H eather G egenhuber, N ancy Kleiman, W illiam Kolling, Kimberly N guyen, and T ien Phan. Particular thanks are offered to Tari Broderick, Senior Acquisitions Editor, and Stephanie Roulias, Product D evelopment Editor, for their support and guidance during the revision process and to the other exceptional people at Wolters Kluwer H ealth | Lippincott W illiams & W ilkins for their work in the design, preparation, and production of this revi- sion. Finally, special appreciation is extended to Tom Conville for his expertise in copyedit- ing and assistance in resource development. H oward C. Ansel Athens, Georgia Shelly J. Stockton Weatherford, Oklahoma vii  Contents Preface v Acknowledgments vii Introduction xi 1 Fundamentals of Pharmaceutical Calculations.........................................................1 2 International System of Units.................................................................................17 3 Pharmaceutical Measurement...............................................................................35 4 Interpretation of Prescriptions and Medication Orders............................................52 5 Density and Specific Gravity..................................................................................77 6 Percent Strength, Ratio Strength, and Other Expressions of Concentration.............88 7 Calculation of Doses: General Considerations.......................................................110 8 Calculation of Doses: Patient Parameters.............................................................129 9 Calculations Involving Units of Activity and Other Measures of Potency................157 10 Selected Clinical Calculations..............................................................................167 11 Isotonic and Buffer Solutions...............................................................................189 12 Electrolyte Solutions: Milliequivalents, Millimoles, and Milliosmoles......................214 13 Intravenous Infusions, Parenteral Admixtures, Rate-of-Flow Calculations.............239 14 Assessment of Nutritional Status, Enteral and Parenteral Nutrition, and the Food Nutrition Label...............................................................................270 15 Altering Product Strength, Use of Stock Solutions, and Problem Solving by Alligation........................................................................................................296 16 Reducing and Enlarging Formulas.......................................................................316 17 Selected Calculations in Contemporary Compounding..........................................323 18 Selected Calculations Involving Veterinary Pharmaceuticals.................................353 19 Selected Calculations Associated with Plant Extractives.......................................362 20 Calculation of Active Drug Moiety........................................................................369 21 Selected Calculations Involving Radiopharmaceuticals.........................................374 ix x Contents 22 Selected Bioavailability and Pharmacokinetic Calculations...................................386 23 Cost Differential Calculations in Drug Therapy.....................................................399 Appendix A Common Systems of Measurement and Intersystem Conversion.......................................................................................405 Appendix B Glossary of Pharmaceutical Dosage Forms and Drug Delivery Systems...............................................................................412 Comprehensive Review Problems........................................................................417 Index...................................................................................................................445 Table of Atomic Weights......................................................................................453  Introduction Scope of Pharmaceutical Calculations T he use of calculations in pharmacy is varied and broad-based. It encompasses calculations performed by pharmacists in traditional as well as in specialized practice settings and within operational and research areas in industry, academia, and government. In the broad context, the scope of pharmaceutical calculations includes computations related to: chemical and physical properties of drug substances and pharmaceutical ingredients; biological activity and rates of drug absorption, bodily distribution, metabolism, and excretion (pharmacokinetics); statistical data from basic research and clinical drug studies; pharmaceutical product development and formulation; prescriptions and medication orders including drug dosage, dosage regimens, and patient adherence to medication treatment plans; pharmacoeconomics; and other areas. For each of these areas, there is a unique body of knowledge. Some areas are foun- dational, whereas others are more specialized, constituting a distinct field of study. T his textbook is foundational, providing the basic underpinnings of calculations applicable to pharmacy practice in community, institutional, and industrial settings. In community pharmacies, pharmacists receive, fill, and dispense prescriptions and pro- vide relevant drug information to ensure their safe and effective use. Prescriptions may call for prefabricated pharmaceutical products manufactured in industry, or, they may call for individual components to be weighed or measured by the pharmacist and compounded into a finished product. In hospitals and other institutional settings, medication orders are entered into a patient’s medical chart, becoming part of the electronic medical record. In the preparation of pharmaceuticals, both medicinal and nonmedicinal materials are used. T he medicinal components (active therapeutic ingredients or AT Is) provide the benefit desired. T he nonmedicinal ingredients (pharmaceutical excipients) are included in a formula- tion to produce the desired pharmaceutical qualities, as physical form, chemical and physical stability, rate of drug release, appearance, and taste, when desired. W hether a pharmaceutical product is produced in the industrial setting or prepared in a community or institutional pharmacy, pharmacists engage in calculations to achieve stan- dards of quality. T he difference is one of scale. In pharmacies, relatively small quantities of medications are prepared and dispensed for specific patients. In industry, large-scale produc- tion is designed to meet the requirements of pharmacies and their patients on a national and even international basis. T he latter may involve the production of hundreds of thousands of dosage units of a specific drug product during a single production cycle. T he preparation of the various dosage forms and drug delivery systems (defined in Appendix B), containing carefully calculated, measured, verified, and labeled quantities of ingredients, enables accu- rate dosage administration. xi xii Introduction A Step-Wise Approach toward Pharmaceutical Calculations Success in performing pharmaceutical calculations is based on: An understanding of the purpose or goal of the problem An assessment of the arithmetic process required to reach the goal An implementation of the correct arithmetic manipulations For many pharmacy students, particularly those without pharmacy experience, dif- ficulty arises when the purpose or goal of a problem is not completely understood. T he background information provided in each chapter is intended to assist the student in under- standing the purpose of each area of calculations. Additionally, the following steps are sug- gested in addressing the calculation problems in this textbook as well as those encountered in pharmacy practice. St ep 1. Take the time necessary to carefully read and thoughtfully consider the prob- lem prior to engaging in computations. An understanding of the purpose or goal of the problem and the types of calculations that are required will provide the needed direction and confidence. S t e p 2. Estimate the dimension of the answer in both quantity and units of measure (e.g., milligrams) to satisfy the requirements of the problem. A section in Chapter 1 provides techniques for estimation. S t e p 3. Perform the necessary calculations using the appropriate method both for efficiency and understanding. For some, this might require a step-wise approach, whereas others may be capable of combining several arithmetic steps into one. Mathematical equations should be used only after the underlying principles of the equation are understood. S t e p 4. Before assuming that an answer is correct, the problem should be read again and all calculations checked. In pharmacy practice, pharmacists are encouraged to have a professional colleague check all calculations prior to completing and dispens- ing a prescription or medication order. Further, if the process involves components to be weighed or measured, these procedures should be double-checked as well. S t e p 5. Finally, consider the reasonableness of the answer in terms of the numerical value, including the proper position of a decimal point, and the units of measure.  1 Fundamentals of Pharmaceutical Calculations Ob j e c t ive s Upon successful completion of this chapter, the student will be able to: D mon ra h u of percent n pharma u al al ula on. Apply h m hod of ratio and proportion n pro l m ol ng. Apply h m hod of dimensional analysis n pro l m ol ng. D mon ra an und r and ng of gn f an f gur. Apply and al da h m hod of estimation n pharma u al al ula on. Pharmaceutical calculations is the area o study that applies the basic principles o mathematics to the preparation and e icacious use o pharmaceutical preparations. It includes calcula- tions rom initial product ormulation through clinical administration and outcomes assessment. Mathematically, pharmacy students beginning use o this textbook are well prepared. T he basic units o measurement and problem-solving methods have been previously learned and are amiliar. T he newness lies in the terminology used and in the understanding o the pharmaceutical/clinical purpose and goal o each computation. Of vital importance is an appreciation of the need for accuracy, as each calculation must be understood to be directly applicable to the health outcomes and safety of patients. T his initial chapter introduces some basic aspects and methods o pharmaceutical calculations. Units of Measurement Pharmacy and all other health pro essions utilize the Inter national Systems of Units (SI), commonly re erred to as the metr ic system. T his amiliar system, with its base units (meter, liter, kilogram) and corresponding subdivisions, is presented in detail in Chapter 2. Pharmaceutical calculations o ten require the accurate conversion o quantities rom a given or calculated unit to another (e.g., milligrams to micrograms). Prof ciency in operating within this system is undamental to the practice o pharmacy. Two other systems o measurement are presented in Appendix A. T he avoirdupois sys- tem is the common system o commerce, which has not ully been replaced in the U nited States by the International System o U nits. Many product designations are dual scale; that is, equivalent SI and common system measures. It is in the common system that goods are packaged and sold by the ounce, pound, pint, quart, and gallon or linearly measured by the inch, oot, yard, and mile. T he apothecaries’ system of measurement is the traditional system o pharmaceutical measurement, which is now largely o historic signi icance. Intersystem con- version remains an exercise in pharmaceutical calculations and is a component o Appendix A. 1 2 Pharma euti al c al ulations Percent T he term per cent and its corresponding sign, % , mean “in a hundred.” So, 50 percent (50%) means 50 parts in each one hundred of the same item. In pharmacy, percent most often is used to: (a) define the concentration or strength of a pharmaceutical preparation (e.g., a 10% ointment), (b) describe the accuracy of a method or procedure (e.g., a 5% error in a measurement or weighing), and (c) quantify a parameter in a clinical study (e.g., 15% of subjects exhibited a particular effect). Calculations relating to subject area (a) are presented in Chapter 6, and those of subject area (b) are presented in Chapter 3. T he following examples demonstrate the use of percent to define a clinical result. (1) During a clinical study involving 2430 subjects, 2% of the subjects developed a headache. How many patients experienced this adverse effect? N OT E: In performing a pharmaceutical calculation, a given percent may be used directly (as when using a calculator), or it may be converted to a ratio or decimal fraction (e.g., 2% = 2/100 = 0.02). 2430 × 2% = 48.6 or 48 patients, or, 2430 × 2/100 = 48.6 or 48 patients, or, 2430 × 0.02 = 48.6 or 48 patients. (2) During a clinical study, 48 out of a total of 2430 patients developed a headache. Calculate the percent of patients who experienced this adverse effect. 48 × 100% = 1.975 or ≈ 2% 2430 Pr a Ct iCe Pr o b l e ms 1. In a clinical study of niacin as a lipid-altering agent, 60% of the 90 patients in the study group developed flushing. Calculate the number of patients having this reaction. 2. In a clinical study of divalproex sodium (D EPAKO T E) in patients prone to migraine headaches, nausea occurred in 62 of 202 patients whereas the use of a placebo resulted in nausea in 8 of 81 patients. Compare these data in terms of percent of subjects reporting nausea in each study group. 3. If a clinical study of a new drug demonstrated that the drug met the effectiveness criteria in 646 patients of the 942 patients enrolled in the study, express these results as a decimal fraction and as a percent. 4. Ritonavir (N O RVIR) oral solution contains, in addition to ritonavir, 43.2% alco- hol and 26.57% propylene glycol. Calculate the quantities of each of these two ingredients in a 240-mL bottle of the oral solution. 5. If a 60-gram tube of an ointment contains 2.5 grams of active ingredient, calculate the percent concentration of active ingredient in the ointment. 6. T he literature for a pharmaceutical product states that 26 patients of the 2103 enrolled in a clinical study reported headache after taking the product. Calculate (a) the decimal fraction and (b) the percentage of patients reporting this adverse response.  1 Fundamentals of Pharma euti al c al ulations 3 Ratio and Proportion Ratio T he relative amount o two quantities (one to the other), is called their r atio. A ratio resembles a common raction except in the manner in which it is presented. For example, the raction ½ may be expressed as the ratio, 1:2, and is not read as “one hal ,” but rather as “one is to two.” Rules governing common ractions apply to ratios. For example, i the two terms o a ratio are either multiplied or divided by the same number, the value remains unchanged. T he value is the quotient o the f rst term divided by the second term. For instance, the value o the ratio 20:4 is 5. I the ratio is multiplied by 4, becoming 80:16, or divided by 4, becoming 5:1, the value remains 5. W hen two ratios have the same value, they are termed equivalent r atios, as is the case with the ratios 20:4, 80:16, and 5:1. As described next, equivalent ratios provide the basis or problem solving by the ratio and proportion method. Proportion A pr opor tion is the expression o the equality o two ratios. It may be written in any one o three standard orms: (1) a : b = c : d (2) a : b :: c : d a c (3) = b d Each o these expressions is read: a is to b as c is to d, and a and d are called the extremes (meaning “outer members”) and b and c the means (“middle members”). In any proportion, the product of the extremes is equal to the product of the means. T his principle allows us to ind the missing term o any proportion when the other three terms are known. I the missing term is a mean, it will be the product of the extremes divided by the given mean, and i it is an extreme, it will be the product of the means divided by the given extreme. U sing this in ormation, we may derive the ollowing ractional equations: a c If = , then b d bc ad ad bc a= , b= , c= , and d =. d c b a In a proportion that is properly set up, the position o the unknown term does not mat- ter. H owever, some persons pre er to place the unknown term in the ourth position—that is, in the denominator o the second ratio. It important to label the units in each position (e.g., mL, mg) to ensure the proper relationship between the ratios of a proportion. T he application o ratio and proportion enables the solution to many o the pharma- ceutical calculation problems in this text and in pharmacy practice. (1) If 3 tablets contain 975 milligrams of aspirin, how many milligrams should be contained in 12 tablets? 3 (tablets ) 975 ( milligrams) = 12 (tablets ) x ( milligrams) 12 (tablets ) × 975 ( milligrams) x ( milligr ams ) = = 3900 milligramss 3 (tablets ) 4 Pharma euti al c al ulations (2) If 3 tablets contain 975 milligrams of aspirin, how many tablets should contain 3900 milligrams? 3 (tablets ) 975 ( milligrams) = x (tablets ) 3900 ( milligrams) 3 ( tablets ) × 3900 ( milligrams) x (tablets ) = = 12 tablets 975 ( milligrams) (3) If 12 tablets contain 3900 milligrams of aspirin, how many milligrams should 3 tablets contain? 12 (tablets ) 3900 ( milligrams) = 3 (tablets ) x ( milligrams) 3 (tablets ) × 3900 ( milligrams) x ( milligrams ) = = 975 milligram ms 12 (tablets ) (4) If 12 tablets contain 3900 milligrams of aspirin, how many tablets should contain 975 milligrams? 12 (tablets) 3900 ( milligrams) = x (tablets) 975 ( milligrams) 12 (tablets) × 975 ( milligrams) x (tablets ) = = 3 tabletss 3900 ( milligrams) Proportions need not contain whole numbers. If common or decimal fractions are supplied in the data, they may be included in the proportion without changing the method. For ease of calculation, it is recommended that common fractions be converted to decimal fractions prior to setting up the proportion. (5) If 30 milliliters (mL) represent 1/6 of the volume of a prescription, how many milliliters will represent ¼ of the volume? 1 = 0.167 and 1 4 = 0.25 6 0.167 ( volume ) 30 ( mL ) = 0.25 ( volume ) x ( mL ) x = 44.91 or ≈ 45 mL Ca l Cu l a t io n s Ca Ps u l e Ratio and Proportion A ratio expresses the relative magnitude of two like quantities (e.g., 1:2, expressed as “1 to 2.”) A proportion expresses the equality of two ratios (e.g., 1:2 = 2:4). The four terms of a proportion are stated as: a c a : b = c : d , or, a : b :: c : d, or = b d and expressed as “a is to b as c is to d.” Given three of the four terms of a proportion, the value of the fourth, or missing, term may be calculated by cross multiplication and solution. The ratio-and-proportion method is a useful tool in solving many pharmaceutical calculation problems  1 Fundamentals of Pharma euti al c al ulations 5 Dimensional Analysis W hen performing pharmaceutical calculations, some students prefer to use a method termed dimensional analysis (also known as factor analysis, factor-label method, or unit-factor method). T his method involves the logical sequencing and placement of a series of ratios (termed factor s) into an equation. T he ratios are prepared from the given data as well as from selected conversion actors and contain both arithmetic quantities and their units of mea- surement. Some terms are inverted (to their reciprocals) to permit the cancellation of like units in the numerator(s) and denominator(s) and leave only the desired terms of the answer. O ne advantage of using dimensional analysis is the consolidation of several arithmetic steps into a single equation. In solving problems by dimensional analysis, the student unfamiliar with the process should consider the following steps1,2: St ep 1. Identify the wanted unit of the answer (e.g., mL, mg, etc.) and place it at the beginning of the equation. Some persons prefer to place a question mark next to it. St ep 2. Identify the given quantity(ies) and its (their) unit(s) of measurement. St ep 3. Identify the conversion factor(s) that is (are) needed for the “unit path” to arrive at the arithmetic answer in the unit wanted. St ep 4. Set up the ratios such that the cancellation of the units of measurement in the numerators and denominators will retain only the wanted unit as identified in Step 1. St ep 5. Perform the arithmetic computation by multiplying the numerators, multiply- ing the denominators, and dividing the product of the numerators by the product of the denominators. T he general scheme shown here and in the “Calculations Capsule: D imensional Analysis” may be helpful in using the method. Unit Path Conversion Factor Conversion Factor Conversion Wanted Quantity Given Quantity as Needed as Needed Computation and Unit (Wanted Unit) = = Example Calculations Using Dimensional Analysis (1) How many f uidounces (f. oz.) are there in 2.5 liters (L)? St ep 1. T he wanted unit for the answer is luidounces. St ep 2. T he given quantity is 2.5 L. St ep 3. T he conversion factors needed are those that will take us from liters to fluidounces. As the student will later learn, these conversion factors are as follows: 1 liter = 1000 mL (to convert the given 2.5 L to milliliters) 1 luidounce = 29.57 mL (to convert milliliters to fluidounces) St ep 4. Set up the ratios in the unit path Unit Path Conversion Factor Conversion Factor Conversion Wanted Quantity Given Quantity as Needed as Needed Computation and Unit fl.oz. (Wanted Unit) = 2.5 L 1000 mL 1 fl. oz. = 1L 29.57 mL 6 Pharma euti al c al ulations N OT E: T he unit path is set up such that all units of measurement will cancel out except for the unit wanted in the answer, fluidounces, which is placed in the numerator. St ep 5. Perform the computation: Unit Path Conversion Factor Conversion Factor Conversion Wanted Quantity Given Quantity as Needed as Needed Computation and Unit 2.5 L 1000 mL 1 fl. oz. 2.5 × 1000 × 1 2500 fl.oz. (Wanted Unit) = = = 84.55 fl. oz. 1L 29.57 mL 1 × 29.57 29.57 or 1000 mL 1 fl. oz. 2.5 × 1000 × 1 2500 2.5 L × × = = = 844.55 fl. oz. 1 L 29.57 mL 1 × 29.57 29.57 N OT E: T he student may wish to see the problem solved by ratio and proportion: St ep 1. 1 (L ) 1000 ( mL ) = ; x = 2500 mL 2.5 ( L ) x (mL ) St ep 2. 29.57 ( mL ) 1( fl. oz. ) = 2500 ( mL ) x ( fl. oz. ) x = 84.55 fl. oz. Ca l Cu l a t io n s Ca Ps u l e Dimensional Analysis An alternative method to ratio and proportion in solving pharmaceutical calculation problems. The method involves the logical sequencing and placement of a series of ratios to consolidate multiple arithmetic steps into a single equation. By applying select conversion factors in the equation—some as reciprocals—unwanted units of measure cancel out, leaving the arithmetic result and desired unit. Dimensional analysis scheme: Unit Path Conversion Factor Conversion Factor Conversion Wanted Quantity Given Quantity as Needed as Needed Computation and Unit (Wanted Unit) = =  1 Fundamen als of Pharma eu al c al ula ons 7 (2) A medication order calls for 1000 milliliters of a dextrose intravenous infusion to be administered over an 8-hour period. Using an intravenous administration set that delivers 10 drops/milliliter, how many drops per minute should be delivered to the patient? Solving by dimensional analysis: 8 hours = 480 minutes (min) 10 drops 1 ? drops = 1000 mL × × = 20.8 or 21 drops per minute 1 mL 480 min N OT E: “drops” was placed in the numerator and “minutes” in the denominator to arrive at the answer in the desired term, drops per minute. T he student may wish to see this problem solved by ratio and proportion: St ep 1. 480 (min) 1000 (mL) = ; x = 2.08 mL 1 (min) x (mL) St ep 2. 1 (mL) 10 (drops) = ; x = 2.08 mL or 21 drops per minute 2.08 (mL) x (drops) T he following problem is often used to demonstrate the process of dimen- sional analysis. (3) Calculate the number of seconds in a day. 24 h 60 min 60 s 24 × 60 × 60 ? s = 1 day × × × =1× = 86, 400 s 1 day 1 h 1 min 1×1×1 Ca s e in Po in t 1.1 A pharma s onsul s w h a paren on he use of a ough syrup for her 5 -year-old h ld. t he nonpres r p on ough syrup on a ns, n ea h 5 -mL (m ll l ers), 1 0 mg (m ll grams) of dex rome horphan Hb r, a ough suppres- san , and 1 0 0 mg of gua fenes n, an expe oran. t he pa kage la el nd a es ha he dose for a h ld 2 o 6 years of age s 1 /4 of he adul dose of wo easpoonfuls. t he pharma s sugges s us ng an oral syr nge al ra ed n 0.2 5 -mL un s for dos ng. if a s andard easpoonful s equ valen o 5 mL, (a) how many m ll l ers should e adm n s ered o he h ld, and ( ) how many m ll grams of ea h of he wo herapeu- ngred en s would e adm n s ered per h ld’s dose? 8 Pharma euti al c al ulations Pr a Ct iCe Pr o b l e ms 1. If an insulin injection contains 100 units of insulin in each milliliter, how many milliliters should be injected to receive 40 units of insulin? 2. An injection contains 2 mg of medication in each milliliter (mL). If a physician prescribes a dose of 0.5 mg to be administered to a hospital patient three times daily, how many milliliters of injection will be required over a 5-day period? 3. In a clinical study, a drug produced drowsiness in 30 of the 1500 patients studied. H ow many patients of a certain pharmacy could expect similar effects, based on a patient count of 100? 4. A formula for 1250 tablets contains 6.25 grams of diazepam. H ow many grams of diazepam should be used in preparing 550 tablets? 5. If 100 capsules contain 400 mg of an active ingredient, how many milligrams of the ingredient will 48 capsules contain? 6. Each tablet of T YLEN O L W IT H CO D EIN E contains 30 mg of codeine phos- phate and 300 mg of acetaminophen. By taking 2 tablets daily for a week, how many milligrams of each drug would the patient take? 7. A cough syrup contains 10 mg of dextromethorphan hydrobromide per 5 mL. H ow many milligrams of the drug are contained in a 120-mL container of the syrup? 8. If an intravenous fluid is adjusted to deliver 15 mg of medication to a patient per hour, how many milligrams of medication are delivered per half minute? 9. T he biotechnology drug filgrastim (N EU PO G EN ) is available in syringes containing 480 micrograms (mcg) of filgrastim per 0.8 mL. H ow many micro- grams of the drug would be administered by each 0.5 mL injection? 10. An oral solution contains, in each milliliter, 80 mg of lopinavir and 20 mg of ritonavir. H ow many milligrams of each drug would be contained in a calculated dose of 0.4 mL? 11. Aripiprazole (ABILIFY) injection is available in single-dose vials containing 9.75 mg of aripiprazole in each 1.3 mL of injection. Calculate the volume of injec- tion that would provide a dose of 5.25 mg of aripiprazole. 12. Acyclovir (ZO VIRAX) suspension contains 200 mg of acyclovir in each 5 mL. H ow many milligrams of acyclovir are contained in a pint (473 mL) of suspension? 13. A metered dose inhaler contains 225 mg of metaproterenol sulfate, which is sufficient for 100 inhalations. H ow many micrograms (mcg) of metaproterenol sulfate would be administered with each inhalation if there are 1000 micrograms in each milligram? 14. A pediatric vitamin drug product contains the equivalent of 0.25 mg of fluoride ion in each milliliter. H ow many milligrams of fluoride ion would be provided by a dropper that delivers 0.6 mL? 15. If a pediatric vitamin contains 1500 units of vitamin A per milliliter of solution, how many units of vitamin A would be administered to a child given 2 drops of the solution from a dropper calibrated to deliver 20 drops per milliliter of solution? 16. An elixir contains 25 mg of drug in each 5 mL. H ow many milligrams of the drug would be used in preparing 4000 mL of the elixir? 17. An elixir of ferrous sulfate contains 220 mg of ferrous sulfate in each 5 mL. If each milligram of ferrous sulfate contains the equivalent of 0.2 mg of elemental iron, how many milligrams of elemental iron would be represented in each 5 mL of the elixir? 18. An estradiol transdermal patch is available in various patch sizes. T he patch size is closely proportional to the amount of drug contained in the patch. If the patch  1 Fundamentals of Pharma euti al c al ulations 9 containing 0.025 mg of estradiol is 6.5 cm 2 in size, calculate the approximate size of the patch containing 0.1 mg of estradiol. 19. If an ophthalmic solution contains 1 mg of dexamethasone phosphate in each milliliter of solution, how many milligrams of dexamethasone phosphate would be contained in 2 drops if the eyedropper used delivered 20 drops per milliliter? 20. A 15-mL package of nasal spray delivers 20 sprays per milliliter of solution, with each spray containing 1.5 mg of drug. (a) H ow many total sprays will the package deliver? (b) H ow many milligrams of drug are contained in the 15-mL package of the spray? 21. A penicillin V potassium preparation provides 400,000 units of activity in each 250-mg tablet. H ow many total units of activity would a patient receive from tak- ing 4 tablets a day for 10 days? 22. If a 5-g packet of a potassium supplement provides 20 milliequivalents of potas- sium ion and 3.34 milliequivalents of chloride ion, (a) how many grams of the powder would provide 6 milliequivalents of potassium ion, and (b) how many milliequivalents of chloride ion would be provided by this amount of powder? 23. If a potassium chloride elixir contains 20 milliequivalents of potassium ion in each 15 mL of elixir, how many milliliters will provide 25 milliequivalents of potassium ion to the patient? 24. T he blood serum concentration of the antibacterial drug ciprofloxacin increases proportionately with the dose of drug administered. If a 250-mg dose of the drug results in a serum concentration of 1.2 micrograms of drug per milliliter of serum, how many micrograms of drug would be expected per milliliter of serum following a dose of 500 mg of drug? 25. T he dosage of the drug thiabendazole (MIN T EZO L) is determined in direct proportion to a patient’s weight. If the dose of the drug for a patient weighing 150 pounds is 1.5 grams, what would be the dose for a patient weighing 110 pounds? 26. If 0.5 mL of a mumps virus vaccine contains 5000 units of antigen, how many units would be present in each milliliter if the 0.5 mL of vaccine was diluted to 2 mL with water for injection? 27. A sample of O riental ginseng contains 0.4 mg of active constituents in each 100 mg of powdered plant. H ow many milligrams of active constituents would be present in 15 mg of powdered plant? N O T E: Solve problems 28 to 32 by dimensional analysis, using the following equivalencies as needed: 1 gram (g) = 1000 milligrams (mg) 1 mg = 1000 micrograms (mcg) 1 kilogram (kg) = 2.2 pounds (lb) 28. If 120 mL of a syrup contains 1.2 g of rimantadine H Cl, and if a 2.5-mL dose of the syrup is administered, how many milligrams of rimantadine H Cl would be given? 29. H ow many milliliters of an injection containing 0.25 mg of drug in each milliliter should be administered to provide a dose of 10 mcg? 30. An injection intended for pediatric use contains 100 mcg of digoxin per milliliter. W hat volume of injection should be administered to provide a dose of 0.04 mg? 31. A patient is to receive 2 mg of drug from an injection labeled to contain 150 mcg/mL. Calculate the milliliters of injection to administer. 32. T he dose of a drug is 0.05 mg for each kilogram of a patient’s weight. T he drug is available as an oral liquid containing 50 mcg/0.1 mL. Calculate the dose of the oral liquid, in milliliters, for a patient who weighs 132 lb. 10 Pharma euti al c al ulations Alligation Alligation is an arithmetic method o solving problems relating mixtures o components o di erent strengths. T here are two types o alligation: alligation medial and alligation alternate. Alligation medial may be used to determine the strength o a common ingredient in a mixture o two or more preparations. For example, i a pharmacist mixed together known volumes o two or more solutions containing known amounts o a common ingredient, the strength o that ingredient in the resulting mixture can be determined by alligation medial. Alligation alternate may be used to determine the proportion or quantities o two or more components to combine in order to prepare a mixture o a desired strength. For example, i a pharmacist wished to prepare a solution o a speci ied strength by combining two or more other solutions o di ering concentrations o the same ingredient, the propor- tion or volumes o each solution to use may be determined by alligation alternate. Alligation medial and alligation alternate may be used as options in solving a number o pharmaceutical calculations problems. T he methods and problem examples are presented in Chapter 15. Significant Figures W hen we count objects accurately, every f gure in the numeral expressing the total number o objects must be taken at its ace value. Such f gures may be said to be absolute. W hen we record a measurement, the last f gure to the right must be taken to be an approximation, an admission that the limit o possible precision or o necessary accuracy has been reached and that any urther f gures to the right would not be signif cant—that is, either meaningless or, or a given purpose, needless. A denominate number, like 325 grams, is interpreted as ollows: T he 3 means 300 grams, neither more nor less, and the 2 means exactly 20 grams more; but the inal 5 means approximately 5 grams more, that is, 5 grams plus or minus some raction o a gram. W hether this raction is, or a given purpose, negligible depends on how precisely the quantity was (or is to be) weighed. Significant figur es, then, are consecutive igures that express the value o a denomi- nate number accurately enough or a given purpose. T he accuracy varies with the number o signi icant igures, which are all absolute in value except the last, and this is properly called uncertain. W hether zero is signi icant, however, depends on its position or on known acts about a given number. T he interpretation o zero may be summed up as ollows: (1) Any zero between digits is signif cant. (2) Initial zeros to the le t o the f rst digit are never signif cant; they are included merely to show the location o the decimal point and thus give place value to the digits that ollow. (3) O ne or more f nal zeros to the right o the decimal point may be taken to be signif cant. Examples: Assuming that the ollowing numbers are all denominate: (1) In 12.5, there are three signif cant f gures; in 1.256, our signif cant f gures; and in 102.56, f ve signif cant f gures. (2) In 0.5, there is one signif cant f gure. T he digit 5 tells us how many tenths we have. T he nonsignif cant 0 simply calls attention to the decimal point. (3) In 0.05, there is still only one signif cant f gure, as there is in 0.005.  1 Fundamentals of Pharma euti al c al ulations 11 (4) In 0.65, there are two signi cant gures, and likewise two in 0.065 and 0.0065. (5) In 0.0605, there are three signi cant gures. T he rst 0 calls attention to the deci- mal point, the second 0 shows the number o places to the right o the decimal point occupied by the remaining gures, and the third 0 signi cantly contributes to the value o the number. In 0.06050, there are four signi cant gures, because the nal 0 also contributes to the value o the number. [It should be noted, however, that in pharmacy practice “trailing zeros” are not retained as a result of a calculation as they may lead to misinterpretation and error.] Ca l Cu l a t io n s Ca Ps u l e Significant Figures Digits other than zero are significant. A zero between digits is significant. Zeros used only to show the location of the decimal point are not significant. The United States Pharmacopeia states that in performing pharmaceutical calcula- tions, all figures are to be utilized until the calculations are completed and then only the significant figures retained in the final result.3 O ne o the actors determining the degree o approximation to per ect measurement is the precision o the instrument used. It would be incorrect to claim that 7. 76 milliliters had been measured in a graduate calibrated in units o 1 milliliter, or that 25.562 grams had been weighed on a balance sensitive to 0.01 gram. We must clearly distinguish significant figures rom decimal places. W hen recording a measurement, the number o decimal places we include indicates the degree of precision with which the measurement has been made, whereas the number o signi icant igures retained indicates the degree of accuracy that is su icient or a given purpose. Sometimes we are asked to record a value “correct to (so many) decimal places.” We should never con use this amiliar expression with the expression “correct to (so many) sig- ni icant igures.” For example, i the value 27.625918 is rounded to five decimal places, it is written 27.62592; but when this value is rounded to five significant figures, it is written 27.626. Rules for Rounding (1) W hen rounding a measurement, retain as many gures as will give only one uncertain gure. For example, in using a ruler calibrated only in ull centimeter units, it would be correct to record a measurement o 11.3 centimeters but not 11.32 centimeters, because the 3 (tenths) is uncertain and no gure should ollow it. (2) W hen eliminating superf uous gures ollowing a calculation, add 1 to the last g- ure retained in a calculation i it is 5 or more. For example, 2.43 may be rounded o to 2.4, but 2.46 should be rounded o to 2.5. (3) W hen adding or subtracting approximate numbers, include only as many decimal places as are in the number with the fewest decimal places. For example, when adding 162.4 grams + 0.489 gram + 0.1875 gram + 120.78 grams, the sum is 283.8565 grams, but the rounded sum is 283.9 grams. H owever, when an instrument has the capa- bility to weigh precisely all the quantities in such a calculation, rounding may be deemed inappropriate. 12 Pharma euti al c al ulations In this regard, there is an assumption made in pharmaceutical calculations that all measurements in the filling of a prescription or in compounding a formula are performed with equal precision by the pharmacist. T hus, or example, i the quantities 5.5 grams, 0.01 gram, and 0.005 gram are speci ied in a ormula, they may be added as i they are precise weights, with a sum o 5.515 grams. (4) W hen multiplying or dividing two approximate numbers, retain no more signif - cant f gures than the number having the ewest signif cant f gures. For example, i multiplying 1.6437 grams by 0.26, the answer may be rounded rom the calculated 0.427362 gram to 0.43 gram. (5) W hen multiplying or dividing an approximate number by an absolute number, the result should be rounded to the same number o signif cant f gures as in the approximate number. T hus, i 1.54 milligrams is multiplied by 96, the product, 243.84 milligrams, may be rounded to 244 milligrams, or to three signif cant f gures. (6) O tentimes, logic plays a role. For example, when a calculation is per ormed to determine the number of doses available rom a medication or the number of drops to be administered to a patient, it is both logical and practical to express the answer in whole units. Pr a Ct iCe Pr o b l e ms 1. State the number o signi icant igures in each o the italicized quantities: (a) O ne luidounce equals 29.57 milliliters. (b) O ne liter equals 1000 milliliters. (c) O ne inch equals 2.54 centimeters. (d) T he chemical costs $1.05 per pound. (e) O ne gram equals 1,000,000 micrograms. ( ) O ne microgram equals 0.001 milligram. 2. Round each o the ollowing to three signi icant igures: (a) 32.75 (b) 200.39 (c) 0.03629 (d) 21.635 (e) 0.00944 3. Round each o the ollowing to three decimal places: (a) 0.00083 (b) 34.79502 (c) 0.00494 (d) 6.12963 4. I a mixture o seven ingredients contains the ollowing approximate weights, what can you validly record as the approximate total combined weight o the ingredients? 26.83 grams, 275.3 grams, 2.752 grams, 4.04 grams, 5.197 grams, 16.64 grams, and 0.085 gram. 5. Per orm the ollowing computations, and retain only signi icant igures in the results: (a) 6.39 – 0.008 (b) 7.01 – 6.0 (c) 5.0 × 48.3 grams (d) 24 × 0.25 gram (e) 56.824 ÷ 0.0905 ( ) 250 ÷ 1.109  1 Fundamentals of Pharma euti al c al ulations 13 Estimation It is important for pharmacy students and pharmacists to recognize the reasonableness of the result of a calculation. By performing an estimation of the answer prior to calculation, the approximate result may be predetermined. T his helps assure the correct dimension of the answer including the critical placement of a decimal point. T he technique of estimation is demonstrated by the examples that follow. Rounding of numbers is a component of this process. Add the following numbers: 7428, 3652, 1327, 4605, 2791, and 4490. Estimation: T he figures in the thousands column add up to 21,000, and with each number on the average contributing 500 more, or every pair 1000 more, we get 21,000 + 3000 = 24,000, estimated answer (actual answer, 24,293). In multiplication, the product of the two leftmost digits plus a sufficient number of zeros to give the right place value serves as a fair estimate. T he number of zeros supplied must equal the total number of all discarded figures to the left of the decimal point. Approximation to the correct answer is closer if the discarded figures are used to round the value of those retained. M ultiply 612 by 413. Estimation: 4 × 6 = 24, and because we discarded four figures, we must supply four zeros, giving 240,000, estimated answer (actual answer, 252,756). In division, the given numbers may be rounded off to convenient approximations, but again, care is needed to preserve the correct place values. Divide 2456 by 5.91. Estimation: T he numbers may be rounded off to 2400 and 6. We may divide 24 by 6 mentally, but we must remember the two zeros substituted for the given 56 in 2456. T he estimated answer is 400 (actual answer, 416). Pr a Ct iCe Pr o b l e ms 1. Estimate the sums: (a) 5641 (b) 3298 (c) $75.82 2177 368 37.92 294 5192 14.69 8266 627 45.98 3503 4835 28.91 49.87 2. Estimate the products: (a) 42 × 39 = (b) 596 × 204 = (c) 8431 × 9760 = (d) 0.0726 × 6951 = (e) 6.1 × 67.39 = 3. Estimate the quotients: (a) 171 ÷ 19 = (b) 184 ÷ 2300 = (c) 98,000 ÷ 49 = (d) 1.0745 ÷ 500 = (e) 458.4 ÷ 8 = 14 Pharma euti al c al ulations Ca l Cq u iz 1.A. Digoxin (LANOXIN) pediatric elixir contains 0.05 mg (milligram) of digoxin in each milliliter (mL) of elixir. If there are 1000 µg (micrograms) in each milligram, how many micrograms of digoxin would be delivered in each dose of 0.6 mL? 1.B. A probiotic colon health product contains, in each capsule, 3 billion viable cells of Lactobacillus acidophilus and Bifidobacterium longum. Express, by exponential notation, the number of viable cells in a container of 30 capsules. 1.C. A liquid dietary supplement is packaged in 10-mL dropper containers to deliver 2000 international units of vitamin D3 in each drop (0.027 mL). Calculate the number of drops delivered per milliliter. 1.D. The drug pramlintide (SYMLIN) is an antihyperglycemic agent for use in patients with diabetes treated with insulin. A 5-mL vial contains 600 µg of pramlintide per milliliter. A 0.05-mL dose measures 5 insulin units on the syringe used for injection and pro- vides 30 µg of pramlintide. Calculate the number of micrograms of pramlintide and the corresponding measurement of insulin units on the syringe with the administra- tion of 0.075 mL of injection. 1.E. A physician prescribed mometasone furoate monohydrate (NASONEX) nasal spray for a patient, with directions to administer two sprays into each nostril once daily. If each spray contains 50 µg of drug and the container can deliver a total of 120 sprays, how many micrograms of drug would the patient receive daily, and how many days of use will the prescription last the patient? a n s w e r s t o “Ca s e in Po in t ” a n d Pr a Ct iCe Pr o b l e ms Case in Point 1.1 1 teaspoonful = 5 mL Adult dose = 2 teaspoonfuls = 10 mL (a) Child’s dose = 1/4 × 10 mL (2 teaspoonfuls) = 2.5 mL 10 mg × 2.5 mL (b) ? mg dextromethorphan H Br = = 5 mg dextromethorphan H Br 5 mL and 100 mg × 2.5 mL ? mg guaifenesin = 5 mL = 50 mg guaifenesin Proof of calculations: child’s dose is ¼ of adult dose: Child’s calculated dose of cough syrup/adult dose = 2.5 mL/10 mL = ¼ √ Child’s calculated dose of dextromethorphan H Br/adult dose = 5 mg/20 mg = ¼ √ Child’s calculated dose of guaifenesin/adult dose = 50 mg/200 mg = ¼ √  1 Fundamentals of Pharma euti al c al ulations 15 Percent 29. 0.04 mL injection 1. 54 patients 30. 0.4 mL injection 2. 30.7% D EPAKO T E subjects 31. 13.3 mL injection 9.9% placebo subjects 32. 6 mL oral liquid 3. 0.69 or 69% Significant Figures 4. 103.68 mL alcohol 1. (a) four 63.77 mL propylene glycol (b) four 5. 4.17% (c) three 6. 0.012 or 1.2% of patients (d) three Ratio, Proportion, and Dimensional (e) seven Analysis (f) one 2. (a) 32.8 1. 0.4 mL insulin injection (b) 200 2. 3.75 mL (c) 0.0363 3. 2 patients (d) 21.6 4. 2.75 g diazepam (e) 0.00944 5. 192 mg 3. (a) 0.001 6. 420 mg codeine phosphate (b) 34.795 4200 mg acetaminophen (c) 0.005 7. 240 mg dextromethorphan hydro- (d) 6.130 bromide 4. 330.8 g 8. 0.125 mg 5. (a) 6.38 9. 300 mcg filgrastim (b) 1.0 10. 32 mg lopinavir and 8 mg ritonavir (c) 240 g 11. 0.7 mL aripiprazole injection (d) 6.0 g 12. 18,920 mg acyclovir (e) 628 13. 2250 mcg metaproterenol sulfate (f) 225 14. 0.15 mg fluoride ion 15. 150 units vitamin A Estimation 16. 20,000 mg 1. (a) 20,500 (19,881) 17. 44 mg elemental iron (b) 14,500 (14,320) 18. 26 cm 2 (c) $240.00 ($253.19) 19. 0.1 mg dexamethasone phosphate 2. (a) 40 × 40 = 1600 (1638) 20. (a) 300 sprays (b) 600 × 200 = 120,000 (121,584) (b) 450 mg (c) 8000 × 10,000 = 80,000,000 21. 16,000,000 units (82,286,560) 22. (a) 1.5 g (d) (7 × 70) = 490 (504.6426) (b) 1 milliequivalent chloride ion (e) 6 × 70 = 420 (411.079) 23. 18.75 mL 3. (a) 170 ÷ 20 = 8.5 (9.0) 24. 2.4 mcg ciprofloxacin (b) 180 ÷ 2000 = 0.09 (0.08) 25. 1.1 g thiabendazole (c) 9800 ÷ 5 = 1960 (2000) 26. 2500 units antigen (d) 0.01 ÷ 5 = 0.002 (0.002149) 27. 0.06 mg (e) 460 ÷ 8 = 57.5 (57.3) 28. 25 mg rimantadine H Cl 16 Pharma euti al c al ulations References 1. D imensional Analysis–Tripod.com. Available at: http:/ / susanp3.tripod.com/ snurse/ id28.htm. Accessed O ctober 16, 2015. 2. Craig G P. Clinical Calculations M ade Easy. 4th Ed. Baltimore, MD : Lippincott W illiams & W ilkins, 2008. 3. T he U nited States Pharmacopeial Convention. United States Pharmacopeia 32 N ational Formulary 27. Rockville, MD : T he U nited States Pharmacopeial Convention, 2009;1:675.  2 International System of Units Ob j e c t ive s Upon successful completion of this chapter, the student will be able to: D mon ra an und r and ng of h in rna onal s y m of Un. c on r m a ur w h n h in rna onal s y m of Un. c on r m a ur w n h in rna onal s y m of Un and o h r y m of m a ur u d n pharma y. Apply h in rna onal s y m of Un n pharma u al al ula on. T he Inter national System of Units (SI), formerly called the metr ic system, is the internationally recognized decimal system of weights and measures. T he system was formu- lated in France in the late 18th century. O ver the years, effort has been made in the U nited States to transition from use of the common systems of weights and measures (e.g., pounds, feet, gallons) to the international system. Today, the pharmaceutical research and manu- facturing industry, the United States Pharmacopeia–N ational Formulary,a and all the health professions reflect conversion to the SI system. T he advantages include the simplicity of the decimal system, the clarity provided by the base units and prefixes, and the ease of scientific and professional communications provided through the use of a universally accepted system. T he base units of the SI are the meter (for length), the kilogram (for weight), and the liter (for volume).b Subdivisions and multiples of these base units, their relative values, and their corresponding prefixes are shown in Table 2.1. Guidelines for the Correct Use of the SI T he following are select guidelines for the correct use of the SI from the U.S. Metric Association, with additional considerations relevant to the practice of pharmacy1,2: U nit names and symbols are not capitalized except when used at the beginning of a sentence or in headings. H owever, the symbol for liter (L, l) may be capitalized or not. For example, for four grams, use 4 g and not 4 G ; for 4 millimeters, use 4 mm and not 4 MM; but, for 4 liters, 4 L or 4 l are acceptable. In the U nited States, the decimal marker (or decimal point) is placed on the line with the number; however, in some countries, a comma or a raised dot is used, for example, 4.5 mL (U nited States) and 4,5 mL or 4 · 5 mL (non-U nited States). a T he United States Pharmacopeia— N ational Formulary (U SP–N F) establishes standards for the quality, purity, and strength of prescription and nonprescription medicines. T hese standards, which are recognized and used by over 140 countries, are published in printed volumes and electronically. T he Authors’ Extra Point at the end of this chapter further describes the USP–N F and other national, regional, and international pharmacopeias. b Although not included in this text, the SI includes measures of force, viscosity, electricity, luminance, and many others in a variety of disciplines. 17 18 Pharma euti al c al ulations Tb 2.1 Pr e f Ixe S a n d r e l a TIve va l Ue S o f Th e In Te r n a TIo n a l SySTe m (SI) P i m i g Sub i isi s atto- one-quintillionth (10 −18 ) of the basic unit femto- one-quadrillionth (10 −15 ) of the basic unit pico- one-trillionth (10 −12 ) of the basic unit nano- one-billionth (10 −9 ) of the basic unit micro- one-millionth (10 −6) of the basic unit milli- one-thousandth (10 −3) of the basic unit centi- one-hundredth (10 −2 ) of the basic unit deci- one-tenth (10 −1 ) of the basic unit mu tip s deca- 10 times the basic unit hecto- 100 times (10 2 ) the basic unit kilo- 1000 times (10 3 ) the basic unit myria- 10,000 times (10 4 ) the basic unit mega- 1 million times (10 6 ) the basic unit giga- 1 billion times (10 9 ) the basic unit tera- 1 trillion times (10 12 ) the basic unit peta- 1 quadrillion times (10 15 ) the basic unit exa- 1 quintillion times (10 18) the basic unit Periods are not used ollowing SI symbols except at the end o a sentence, for example, 4 mL and 4 g, not 4 mL. and 4 g. A compound unit that is a ratio or quotient o two units is indicated by a solidus (/) or a negative exponent, for example, 5 mL/h or 5 mL·h −1. Symbols should not be combined with spelled-out terms in the same expression, for example, 3 mg/mL, not 3 mg/milliliter. Plurals o unit names, when spelled out, have an added “s.” Symbols or units, however, are the same in singular and plural, for example, 5 milliliters or 5 mL, not 5 mLs. Two symbols exist or microgram: mcg (o ten used in pharmacy practice) and mg (SI). T he symbol or square meter is m 2; or cubic centimeter, cm 3; and so orth. In pharmacy practice, a cubic centimeter (cm 3) is considered equivalent to a milliliter.2 T he symbol “cc,” or cubic centimeter, is not an accepted SI symbol. D ecimal ractions are used, not common ractions, for example, 5.25 g, not 5¼ g. A zero always should be placed in ront o a leading decimal point to prevent medication errors caused by uncertain decimal points, for example, 0.5 g, not.5 g. It is cr itically impor tant for phar macists to recognize that a misplaced or misr ead decimal point can lead to an er r or in calculation of a minimum of one-tenth or 10 times the desir ed quantity. To prevent misreadings and medication errors, “trailing” zeros should not be placed ollowing a whole number on prescriptions and medication orders, for example, 5 mg, not 5.0 mg. H owever, in some tables (such as those o the SI in this chapter), phar- maceutical ormulas, and quantitative results, trailing zeros o ten are used to indicate exactness to a specif c number o decimal places. In selecting symbols o unit dimensions, the choice generally is based on selecting the unit that will result in a numeric value between 1 and 1000, for example, 500 g, rather than 0.5 kg; 1.96 kg, rather than 1960 g; and 750 mL, rather than 0.75 L.  2 internat onal s y tem of Un t 19 Special Considerations of the SI in Pharmacy Although some remnants o the common systems o measurement (see Appendix A) in pharmacy remain, the use o the SI is nearly total. T he system is used to manu acture and label pharmaceutical products (Fig. 2.1); write, f ll, and compound prescriptions and insti- tutional medication orders; dose patients; express clinical laboratory test results; and com- municate both verbally and through scientif c and pro essional literature. In the large-scale manu acture o dosage orms, pharmaceutical ingredients are measured in kilogram and kiloliter quantities. In the community and institutional phar- macy, compounding and dispensing in milligram, gram, and milliliter quantities are more common. D rug doses are typically administered in milligram or microgram amounts and prepared in solid dosage orms, such as tablets or capsules, or in a stated volume o a liquid preparation, such as an oral solution (e.g., 30 mg/5 mL) or injection (e.g., 2 mg/mL). D oses or certain drugs are calculated on the basis o body weight and expressed as mg/kg, mean- ing a certain number o milligrams of drug per kilogram of body weight. Clinical laboratory values are in metric units and expressed, or example, as mg/dL, meaning milligrams of drug per deciliter of body fluid (such as blood). Particle Size and Nanotechnology D rug particle size has long been an important consideration in pharmaceutical technology. T hrough the milling and reduction o drug materials to micron size, the sur ace area o particles is increased (Fig. 2.2) and pharmaceutical and clinical benef ts o ten accrue. T hese benef ts may include the ollowing3: Increased aqueous dissolution rates or poorly soluble substances Improved bioavailability, with increased rates o absorption o orally administered drugs Lower oral dosage possibilities with enhanced drug absorption Expanded ormulation options in the preparation o stable and predictable phar- maceutical suspensions and colloidal dispersions or all routes o administration, including oral, parenteral, respiratory, ophthalmic, and nasal. f IGUr e 2.1 Example of a pharmaceutical product with the label indicating the strength and quantity (50 mg/10 mL) in SI or metric units. (Reprinted with permission from Lacher BE. Pharmaceutical Calculations for the Pharmacy Technician. Philadelphia, PA: Lippincott Williams & Wilkins; 2007.) 20 Pharma euti al c al ulations Tota l s urfa ce a re a Tota l s urfa ce a re a Tota l s urfa ce a re a 6 cm 2 12 cm 2 24 cm 2 f IGUr e 2.2 Depiction of increased surface area by particle size reduction. (Adapted from company litera- ture, Nanocrystal, Elan Drug Delivery, Inc.) An area of technology with great potential is nanotechnology. Nanotechnology centers on the understanding and control of matter between approximately 1 and 100 nanometers (nm) in size, referred to as the nanoscale range.4 For perspective, a nanometer is one- billionth of a meter; about 25,400,000 nm equals 1 inch; the helix of D N A has a diameter of about 2 nm; and a typical bond between two atoms is about 0.15 nm.5 N anotechnology has applications for many potential products, including those that integrate chemistry, the biological sciences, medicine, and computer technology. Measure of Length T he meter is the primary unit of length in the SI. T he table of metric length: 1 kilometer (km) = 1,000,000 meters 1 hectometer (hm) = 100,000 meters 1 decameter (dam) = 10,000 meters 1 meter (m) 1 decimeter (dm) = 0.100 meter 1 centimeter (cm) = 0.010 meter 1 millimeter (mm) = 0.001 meter 1 micrometer (mm) = 0.000,001 meter 1 nanometer (nm) = 0.000,000,001 meter T he table may also be written: 1 meter = 0.001 kilometer 0.01 hectometer 0.1 decameter 10 decimeters 100 centimeters 1000 millimeters 1,000,000 micrometers 1,000,000,000 nanometers Examples of the use of linear measurement in pharmacy include the dimensions of transdermal skin patches, expressed in cm 2; the use of a patient’s height and weight in calculating the doses of certain drugs; and the clinical reference to the size of a patient’s physical structure, as a tumor, usually measured in mm or cm. As a point of reference, 1 inch is equivalent to 2.54 centimeters or 25.4 millimeters (Fig. 2.3).  2 internat onal s y tem of Un t 21 f IGUr e 2.3 Ruler calibrated in millimeter, centimeter, and inch units. (Courtesy of Schlenker Enterprise, Ltd.) Another application of linear measurement is in distance exercise, undertaken as a component of maintaining good health status. T hese programs are typically measured by both time and dis- tance in miles or kilometers, the relationship of which is demonstrated in Table 2.2. Measure of Volume T he liter is the primary unit of volume. It represents the volume of the cube of one-tenth of a meter, that is, of 1 dm 3. T he table of metric volume: 1 kiloliter (kL) = 1000,000 liters 1 hectoliter (hL) = 100,000 liters 1 decaliter (daL) = 10,000 liters 1 liter (L) 1 deciliter (dL) = 0.100 liter 1 centiliter (cL) = 0.010 liter 1 milliliter (mL) = 0.001 liter 1 microliter (mL) = 0.000,001 liter T his table may also be written: 1 liter = 0.001 kiloliter 0.010 hectoliter 0.100 decaliter 10 deciliters 100 centiliters 1000 milliliters 1,000,000 microliters Although not precisely equivalent, the milliliter is so nearly the same volume as the cubic centimeter (cm 3, cc), the United States Pharmacopeia–N ational Formulary states: “O ne milliliter (mL) is used herein as the equivalent of 1 cubic centimeter (cc).”2 Measurement of volume is commonplace for the pharmacist in preparing and dispens- ing liquid medications and for the patient in measuring dosage. Examples of pharmaceutical graduates for measuring volume are shown in Figure 2.4. Tb 2.2 d e mo n STr a TIo n S o f l In e a r r e l a TIo n Sh IPS f t y s mi s m t s Ki t s 1 mile 5280 1760 1 1609.3 1.6093 1 kilometer 3280.8 1093.6 0.62137 1000 1 22 Pharma euti al c al ulations f IGUr e 2.4 Examples of metric-scale cylindrical (A) and conical pharmaceutical graduates (B). (Courtesy of Kimble/ Kontes Glass.) Measure of Weight T he primary unit of weight in the SI is the gram, which is the weight of 1 cm 3 of water at 4°C, its temperature of greatest density. For practical purposes, 1 cm 3 of water ≈ 1 mL ≈ 1 g of weight. T he table of metric weight: 1 kilogram (kg) = 1,000,000 grams 1 hectogram (hg) = 100,000 grams 1 dekagram (dag) = 10,000 grams 1 gram (g) 1 decigram (dg) = 0.100 gram 1 centigram (cg) = 0.010 gram 1 milligram (mg) = 0.001 gram 1 microgram (mg or mcg) = 0.000,001 gram 1 nanogram (ng) = 0.000,000,001 gram 1 picogram (pg) = 0.000,000,000,001 gram 1 femtogram (fg) = 0.000,000,000,000,001 gram T his table may also be written: 1 gram = 0.001 kilogram 0.010 hectogram 0.100 decagram 10 decigrams 100 centigrams 1000 milligrams 1,000,000 micrograms 1,000,000,000 nanograms 1,000,000,000,000 picograms 1,000,000,000,000,000 femtograms  2 internat onal s y tem of Un t 23 T he weighing of components in the manufacture of a pharmaceutical product and in the compounding of a prescription or medication order is a usual function of a pharmacist. And, since most therapeutic agents are solid substances (i.e., powders), their doses are deter- mined and expressed in units of weight, most often in milligrams. An example of a metric set of weights is shown in Chapter 3. Prescription Writing Style Using the SI Prescriptions written in the SI use Arabic numerals before the abbreviations for the denomi- nations (e.g., 6 g). Q uantities of weight are usually written as grams and decimals of a gram, and volumes as milliliters and decimals of a milliliter: D extromethorphan H Br 320 mg G uaifenesin 3.2 g Cherry syrup, to make 240 mL Fundamental Computations Reducing SI Units to Lower or Higher Denominations by Using a Unit Position Scale T he metric system is based on the decimal system; therefore, conversion from one denomi- nation to another can be done simply by moving the decimal point as demonstrated in Figure 2.5. To change a metr ic denomination to the next smaller denomination, move the deci- mal point one place to the r ight. To change a metr ic denomination to the next lar ger denomination, move the decimal point one place to the left. kg hg da g g dg cg mg (0.1 mg) (0.01 mg) mg 9.876 g 1.23 kg 98.76 dg 12.3 hg 987.6 cg 123.0 da g 9876.0 mg 1230.0 g De cima l Move me nt To Conve rt From La rge r to S ma lle r Units To Conve rt From S ma lle r to La rge r Units f IGUr e 2.5 Position scale of units of weight. 24 Pharma euti al c al ulations (1) Reduce 1.23 kilograms to grams. 1.23 kg = 1230 g (2) Reduce 9876 milligrams to grams. 9876 mg = 9.876 g In the first example, 1.23 kg is to be converted to grams. O n the scale, the gram position is three decimal positions from the kilogram position. T hus, the decimal point is moved three places toward the right. In the second example, the conversion from milligrams also requires the movement of the decimal point three places, but this time to the left. (3) Reduce 85 micrometers to centimeters. 85 mm = 0.085 mm = 0.0085 cm (4) Reduce 2.525 liters to microliters. 2.525 L = 2525 mL = 2,525,000 mL The 3-Decimal Point Shift In pharmacy practice, and health care in general, the denominations most used differ by 1000 or by a factor of 3 decimal places. T hus, on the decimal scale (Fig. 2.5), a 3-place deci- mal point shift, left to right or right to left, will yield most commonly used denominations. 3-Place Shift for Common Weight D enominations: kilograms (kg) _ _ _ grams (g) _ _ _ milligrams (mg) _ _ _ micrograms (mcg) 3-Place Shift for Common Volume D enominations: liters (L) _ _ _ milliliters (mL) Reducing SI Units to Lower or Higher Denominations by Ratio and Proportion or by Dimensional Analysis (5) Reduce 1.23 kilograms to grams. From the table: 1 kg = 1000 g By ratio and proportion: 1 kg 1.23 kg = ; x = 1230 g 1000 g xg By dimensional analysis: 1000 g 1.23 kg × = 1230 g 1 kg (6) Reduce 62,500 mcg to g. From the table: 1 g = 1,000,000 mcg By ratio and proportion: 1, 000, 000 mcg 62, 500 mcg = ; x = 0.0625 g 1g xg By dimensional analysis: 1g 62, 500 mcg × = 0.0625 g 1, 000, 000 mcg  2 internat onal s y tem of Un t 25 Ca l CUl a TIo n S Ca PSUl e International System of Units (SI) The SI or decimal system of measurement is used in the practice of pharmacy and throughout the pharmaceutical industry. The primary SI units for calculating mass or weight (gram), volume (liter), and length (meter) are used along with prefixes to indicate multiples or subdivisions of the primary units. To change an SI denomination to the next smaller denomination, the decimal point is moved one place to the right: gram (g) > d ec igram (d g > c entigram (c g > milligram (mg) 5.555 g = 55.55 dg = 555.5 cg = 5555 mg Each value is equivalent. To change an SI denomination to the next larger denomination, the decimal point is moved one place to the left: kilogram(kg) > hec togram(hg) > d ekagram(d ag) > gram(g) 5.555 kg = 55.55 hg = 555.5 dag = 5555 g Each value is equivalent. A unit position scale (e.g., see Fig. 2.5), ratio and proportion, or dimensional analysis may be used to change denominations. Only numbers of the same denomination may be added to or subtracted from one another. Recognizing Equivalent Expressions O n occasion, it may be necessary to recognize, or prove by calculation, equivalent expres- sions. For example, a given quantity expressed in terms of “mg/100 mL” is equivalent to “mg/dL.” Practice problems (#47 to #50) at the conclusion of this chapter provide exercises to determine equivalent expressions. Addition and Subtraction To add or subtract quantities in the SI, reduce them to a common denomination, preferably a base unit, and arrange their denominate numbers for addition or subtraction as ordinary decimals. (1) Add 1 kg, 250 mg, and 7.5 g. Express the total in grams. 1 kg = 1000. g 250 mg = 0.25 g 7.5 g = 7.5 g 1007.75 g or 1008 g 26 Pharma eu i al c al ula ions (2) Add 4 L, 375 mL, and 0.75 L. Express the total in milliliters. 4L = 4000 mL 375 mL = 375 mL 0.75 L = 750 mL 5125 mL (3) A capsule contains the following amounts of medicinal substances: 0.075 g, 20 mg, 0.0005 g, 4 mg, and 500 mg. W hat is the total weight of the substances in the capsule? 0.075 g = 0.075 g 20 mg = 0.02 g 0.0005 g = 0.0005 g 4 mg = 0.004 g 500 mg = 0.0005 g 0.1000 g or 100 mg (4) Subtract 2.5 mg from 4.85 g. 4.85 g = 4.85 g 2.5 mg = −0.0025 g 4.8475 g or 4.848 g (5) A prescription calls for 0.06 g of one ingredient, 2.5 mg of another, and enough of a third to make 0.5 g. How many milligrams of the third ingredient should be used? 1st ingredient : 0.06 g = 0.06 g 2nd ingredient : 2.5 mg = 0.0025 g 0.0625 g T otal weight : 0.5 g W eight of 1st and 2nd : −0.0625 g W eight of 3rd : 0.4375 g or 437.5 mg Multiplication and Division Because every measurement in the SI is expressed in a single given denomination, prob- lems involving multiplication and division are solved by the methods used for any decimal numbers. (1) M ultiply 820 mL by 12.5 and express the result in liters. 820 mL × 12.5 = 10250 mL = 10.25 L (2) Divide 0.465 g by 15 and express the result in milligrams. 0.465 g ÷ 15 = 0.031 g = 31 mg Ca Se In Po In T 2.1 A nurse elephones a pharma y regarding he proper quan- i y of an inje ion o adminis er o a pedia ri pa ien from a 1 -mL vial on aining 0.1 mg of digoxin. t he a ending physi ian had pres ribed a dose of 2 5 m g. How many millili ers should be he pharma is ’s response?  2 internat onal s y tem of Un t 27 Relation of the SI to Other Systems of Measurement In addition to the International System of U nits, the pharmacy student should be aware of two other systems of measurement: the avoir dupois and apothecar ies’ systems. T he avoirdu- pois system, widely used in the U nited States in measuring body weight and in selling goods by the ounce or pound, is slowly giving way to the international system. T he apothecaries’ system, once the predominant pharmacist’s system of volumetric and weight measure, has also largely been replaced by the SI. T he pharmacist must still appreciate the relationship between the various systems of measurement, however, and deal effectively with them as the need arises. T he avoirdupois and apothecaries’ systems of measurement, including all necessary equivalents and methods for intersystem conversion, are presented in Appendix A. T he example equivalents presented in Table 2.3 are useful in gaining perspective and in solv- ing certain problems in the text—for example, when there is need to convert fluid ounces to milliliters or kilograms to pounds. T hese equivalents should be committed to memory. W hen quantities in units of the apothecaries’ or avoirdupois systems of measurement (see Appendix A) are encountered, it is suggested that they be converted to equivalent quantities in SI units and the required calculation then solved in the usual manner. Example Problems (1) An injection contains 5 mg of drug in each 10-mL vial. If the dose of the drug for a patient is determined to be 150 mg, how many milliliters should be administered? 10 mL 1 mg 150 mg × × = 0.3 mL 5 mg 1000 mg Tb 2.3 So me USe f Ul e q UIva l e n TS e ui ts gth 1 inch = 2.54 cm 1 meter (m) = 39.37 in e ui ts u 1 fluid ounce (fl. oz.) = 29.57 mL 1 pint (16 fl. oz.) = 473 mL 1 quart (32 fl. oz.) = 946 mL 1 gallon, United States (128 fl. oz.) = 3785 mL 1 gallon, United Kingdom = 4545 mL e ui ts w ight 1 pound (lb, avoirdupois) = 454 g 1 ounce (oz, avoirdupois) = 28.35 g 1 kilogram (kg) = 2.2 lb 28 Pharma eu i al c al ula ions (2) A patient is determined to have a total serum cholesterol level of 240 mg/dL. W hat is the equivalent value in mg/100 mL? 1 dL = 100 mL; thus, 240 mg/dL = 240 mg/100 mL (3) T he dose of a drug is 0.5 mg/kg of body weight/day. W hat is the equivalent dose in mg/lb/ day? 0.5 mg = 500 mg 1 kg = 2.2 lb T hus, 0.5 mg/kg/day = 500 mg/2.2 lb/day = 227.3 mg/lb/day (4) An oral suspension contains 1.5 g of the therapeutic agent in a pint of the suspension. Calculate the quantity of therapeutic agent, in milligrams, present in each 5-mL dose. 1.5 g 1000 mg 1 pt ? mg = 5 mL ´ ´ ´ = 15.86 or 15.9 mg 1 pt 1g 473 mL O r, by ratio and proportion: 1.5 g = 1500 mg 1 pint = 473 mL 1500 mg x mg = ; x = 15.86 or 15.9 mg 473 mL 5 mL Ca Se In Po In T 2.2 A hospi al pharma is is asked o prepare an in ravenous infusion of dopamine. b ased on he pa ien ’s weigh , he pharma is al ula es a dose of 5 0 0 m g/min for on inuous infusion. t he on en ra ion of a premixed dopamine infusion is 4 0 0 mg/2 5 0 mL. Wha is he on en ra ion of he infusion on a m g/mL asis? How many milligrams of dopamine is he pa ien o re eive in he firs hour of rea men ? How long will he infusion las ? Pr a CTICe Pr o b l e mS 1. W hat is the weight, in milligrams, of 100 tablets, each containing 20 mcg of a therapeutic agent? 2. Add 7.25 L and 875 cL. Reduce the result to milliliters. 3. Add 0.0025 kg, 1750 mg, 2.25 g, and 825,000 mg, and express the answer in grams. 4. Reduce 1.256 g to micrograms, to milligrams, and to kilograms. 5. Are the terms mcg/mL and mg/L equivalent or not equivalent? 6. A low-strength aspirin tablet contains 81 mg of aspirin per tablet. H ow many tablets may a manufacturer prepare from 0.5 kg of aspirin? 7. Adhesive tape made from fabric has a tensile strength of not less than 20.41 kg/2.54 cm of width. Reduce these quantities to grams and millimeters. 8. In a clinical study, the drug methotrexate produced a blood level of 6.6 mg of methotrexate in each milliliter of blood (6.6 mg/mL). Express the methotrexate blood level in terms of mg/dL.  2 internat onal s y tem of Un t 29 9. An inhalation aerosol contains 225 mg of metaproterenol sulfate, which is sufficient for 300 inhalations. H ow many micrograms of metaproterenol sulfate would be contained in each inhalation? 10. T RIPH ASIL-28 birth control tablets are taken sequentially, 1 tablet per day for 28 days, with the tablets containing the following: Phase 1—6 tablets, each containing 0.05 mg levonorgestrel and 0.03 mg ethinyl estradiol Phase 2—5 tablets, each containing 0.075 mg levonorgestrel and 0.04 mg ethinyl estradiol Phase 3—10 tablets, each containing 0.125 mg levonorgestrel and 0.03 mg ethinyl estradiol; then, 7 inert tablets (no drug). H ow many total milligrams each of levonorgestrel and ethinyl estradiol are taken during the 28-day period? 11. CO LCRYS scored tablets each contain 0.6 mg of colchicine. H ow many micro- grams of colchicine would a patient take by administering one-half tablet? 12. T he following clinical laboratory data are within normal values for an adult. Convert each value to mcg/mL: (a) Ammonia, 30 mcg/dL (b) Folate, 18 pg/mL (c) Serum creatinine, 1.0 mg/dL (d) Prostate-specific antigen (PSA), 3 ng/mL (e) Cholesterol, total, 150 mg/dL 13. T he package insert for D O N N ATAL EXT EN TABS indicates the amount of phenobarbital present in each tablet, in milligrams and in the equivalent weight (3/4 gr