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Chapter 5 Basic Pharmaceutical Measurements and Calculations Learning Objectives • Describe four systems of measurement commonly used in pharmacy, and be able to convert units from one system to another. • Explain the meanings of the prefixes most commonly used in metric measurement. • Convert from one metric unit to another (e.g., grams to milligrams). • Convert Roman numerals to Arabic numerals. Learning Objectives • Distinguish between proper, improper, and compound fractions. • Perform basic operations with fractions, including finding the least common denominator; converting fractions to decimals; and adding, subtracting, multiplying, and dividing fractions. Learning Objectives • Perform basic operations with proportions, including identifying equivalent ratios and finding an unknown quantity in a proportion. • Convert percents to and from fractions and ratios, and convert percents to decimals. • Perform elementary dose calculations and conversions. • Solve problems involving powder solutions and dilutions. • Use the alligation method. SYSTEMS OF PHARMACEUTICAL MEASUREMENT • Metric System • Common Measures • Numeral Systems BASIC MATHEMATICS USED IN PHARMACY PRACTICE • Fractions • Decimals • Ratios and Proportions COMMON CALCULATIONS IN THE PHARMACY • Converting Quantities between the Metric and Common Measure Systems • Calculations of Doses • Preparation of Solutions SYSTEMS OF PHARMACEUTICAL MEASUREMENT • Metric System • Common Measures • Numeral Systems Measurements in the Metric System (a) Distance or length (b) Area (c) Volume Table 5.1 Système International Prefixes Prefix Meaning micro- one millionth (basic unit × 10–6, or unit × 0.000,001) milli- one thousandth (basic unit × 10–3, or unit × 0.001) centi- one hundredth (basic unit × 10–2, or unit × 0.01) deci- one tenth (basic unit × 10–1, or unit × 0.1) hecto- one hundred times (basic unit × 102, or unit × 100) kilo- one thousand times (basic unit × 103, or unit × 1000) Table 5.2 Common Metric Units: Weight Basic Unit Equivalent 1 gram (g) 1000 milligrams (mg) 1 milligram (mg) 1 kilogram (kg) 1000 micrograms (mcg), one thousandth of a gram (g) 1000 grams (g) Table 5.2 Common Metric Units: Length Basic Unit Equivalent 1 meter (m) 100 centimeters (cm) 1 centimeter (cm) 0.01 m 10 millimeters (mm) 0.001 m 1 millimeter (mm) 1000 micrometers or microns (mcm) Table 5.2 Common Metric Units: Volume Basic Unit Equivalent 1 liter (L) 1000 milliliters (mL) 1 milliliter (mL) 0.001 L 1000 microliters (mcL) Measurement and Calculation Issues Safety Note! It is extremely important that decimals be written properly. An error of a single decimal place is an error by a factor of 10. Table 5.3 Common Metric Conversions Conversion Instruction Example kilograms (kg) to grams (g) multiply by 1000 (move decimal point three places to the right) 6.25 kg = 6250 g grams (g) to milligrams (mg) multiply by 1000 (move decimal point three places to the right) 3.56 g = 3560 mg milligrams (mg) to grams (g) multiply by 0.001 (move decimal point three places to the left) 120 mg = 0.120 g Table 5.3 Common Metric Conversions Conversion Instruction Example liters (L) to milliliters (mL) multiply by 1000 (move decimal point three places to the 2.5 L = 2500 mL right) milliliters (mL) to liters (L) multiply by 0.001 (move decimal point three places to the 238 mL = 0.238 L left) Table 5.4 Apothecary Symbols Volume Unit of measure Weight Symbol Unit of measure minim ♏ grain fluidram fℨ scruple fluidounce f℥ dram pint pt ounce quart qt pound gallon gal Symbol gr Э ℨ ℥ ℔ or # Table 5.5 Apothecary System: Volume Measurement Unit Equivalent within System Metric Equivalent 1♏ 0.06 mL 16.23 ♏ 1 mL 1 fℨ 60 ♏ 5 mL (3.75 mL)* 1f ℥ 6 fℨ 30 mL (29.57 mL)† 1 pt 16 f ℥ 480 mL 1 qt 2 pt or 32 f ℥ 960 mL 1 gal 4 qt of 8 pt 3840 mL * In reality, 1 fℨ contains 3.75 mL; however that number is usually rounded up to 5 mL or one teaspoonful †In reality, 1 f℥, contains 29.57 mL; however, that number is usually rounded up to 30 mL. Table 5.5 Apothecary System: Weight Measurement Unit 1 gr 15.432 gr 1Э 1ℨ 1℥ 1# Equivalent within System 20 gr 3 Э or 60 gr 8 ℨ or 480 gr 12 ℥or 5760 gr Metric Equivalent 65 mg 1g 1.3 g 3.9 g 30 g (31.1 g) 373.2 g Measurement and Calculation Issues Safety Note! For safety reasons, the use of the apothecary system is discouraged. Use the metric system instead. Table 5.6 Avoirdupois System Measurement Unit 1 gr (grain) 1 oz (ounce) 1 lb (pound) Equivalent within System Metric Equivalent 437.5 gr 16 oz or 7000 gr 65 mg 30 g (28.35 g)* 1.3 g * In reality, an avoirdupois ounce actually contains 28.34952 g; however, we often round up to 30 g. It is common practice to use 454 g as the equivalent for a pound (28.35 g × 16 oz/lb = 453.6 g/lb, rounded to 454 g/lb). Table 5.7 Household Measure: Volume Measurement Unit Equivalent within System 1 tsp (teaspoonful) Metric Equivalent 5 mL 1 tbsp (tablespoonful) 3 tsp 15 mL 1 fl oz (fluid ounce) 2 tbsp 30 mL (29.57 mL)* 1 cup 8 fl oz 240 mL 1 pt (pint) 2 cups 480 mL* 1 qt (quart) 2 pt 960 mL 1 gal (gallon) 4 qt 3840 mL * In reality, 1 fl oz (household measure) contains less than 30 mL; however, 30 mL is usually used. When packaging a pint, companies will typically present 473 mL, rather than the full 480 mL, thus saving money over time. Table 5.7 Household Measure: Weight Measurement Unit 1 oz (ounce) 1 lb (pound) 2.2 lb Equivalent within System 16 oz Metric Equivalent 30 g 454 g 1 kg Measurement and Calculation Issues Safety Note! New safety guidelines are discouraging use of Roman numerals. Table 5.8 Comparison of Roman and Arabic Numerals Roman Arabic Roman Arabic ss 0.5 or 1/2 L or l 50 I or i or i 1 C or c 100 V or v 5 D or d 500 X or x 10 M or m 1000 Terms to Remember • metric system • meter • gram • liter BASIC MATHEMATICS USED IN PHARMACY PRACTICE • Fractions • Decimals • Ratios and Proportions Fractions • When something is divided into parts, each part is considered a fraction of the whole. Fractions • When something is divided into parts, each part is considered a fraction of the whole. • If a pie is cut into 8 slices, one slice can be expressed as 1/8, or one piece (1) of the whole (8). Fractions of the Whole Pie Fractions If we have a 1000 mg tablet, • ½ tablet = 500 mg • ¼ tablet = 250 mg Terminology fraction a portion of a whole that is represented as a ratio Fractions Fractions have two parts, Fractions Fractions have two parts, • Numerator (the top part) 1 8 Fractions Fractions have two parts, • Numerator (the top part) • Denominator (the bottom part) 1 8 Terminology numerator the number on the upper part of a fraction Terminology denominator the number on the bottom part of a fraction Fractions A fraction with the same numerator and same denominator has a value equivalent to 1. In other words, if you have 8 pieces of a pie that has been cut into 8 pieces, you have 1 pie. 8 1 8 Discussion What are the distinguishing characteristics of the following? • proper fraction • improper fraction • mixed number Remember The symbol > means “is greater than.” The symbol > means “is less than.” Terminology proper fraction 1 1 4 • a fraction with a value of less than 1 • a fraction with a numerator value smaller than the denominator’s value Terminology improper fraction • a fraction with a value of larger than 1 • a fraction with a numerator value larger than the denominator’s value 6 1 5 Terminology mixed number a whole number and a fraction 1 5 2 Adding or Subtracting Fractions When adding or subtracting fractions with unlike denominators, it is necessary to create a common denominator. Adding or Subtracting Fractions When adding or subtracting fractions with unlike denominators, it is necessary to create a common denominator. This is like making both fractions into the same kind of “pie.” Terminology common denominator a number into which each of the unlike denominators of two or more fractions can be divided evenly Remember Multiplying a number by 1 does not change the value of the number. 5 1 5 Therefore, if you multiply a fraction by a fraction that equals 1 (such as 5/5), you do not change the value of a fraction. 5 5 5 5 Guidelines for Finding a Common Denominator 1. Examine each denominator in the given fractions for its divisors, or factors. Guidelines for Finding a Common Denominator 1. Examine each denominator in the given fractions for its divisors, or factors. 2. See what factors any of the denominators have in common. Guidelines for Finding a Common Denominator 1. Examine each denominator in the given fractions for its divisors, or factors. 2. See what factors any of the denominators have in common. 3. Form a common denominator by multiplying all the factors that occur in all of the denominators. If a factor occurs more than once, use it the largest number of times it occurs in any denominator. Example 1 Find the least common denominator of the following fractions Step 1. Find the prime factors (numbers divisible only by 1 and themselves) of each denominator. Make a list of all the different prime factors that you find. Include in the list each different factor as many times as the factor occurs for any one of the denominators of the given fractions. The prime factors of 28 are 2, 2, and 7 (because 2 3 2 3 7 5 28). The prime factors of 6 are 2 and 3 (because 2 3 3 5 6). The number 2 occurs twice in one of the denominators, so it must occur twice in the list. The list will also include the unique factors 3 and 7; so the final list is 2, 2, 3, and 7. Example 1 Find the least common denominator of the following fractions Step 2. Multiply all the prime factors on your list. The result of this multiplication is the least common denominator. Example 1 Find the least common denominator of the following fractions Step 3. To convert a fraction to an equivalent fraction with the common denominator, first divide the least common denominator by the denominator of the fraction, then multiply both the numerator and denominator by the result (the quotient). The least common denominator of 9⁄28 and 1⁄6 is 84. In the first fraction, 84 divided by 28 is 3, so multiply both the numerator and the denominator by 3. Example 1 Find the least common denominator of the following fractions In the second fraction, 84 divided by 6 is 14, so multiply both the numerator and the denominator by 14. Example 1 Find the least common denominator of the following fractions The following are two equivalent fractions: Example 1 Find the least common denominator of the following fractions Step 4. Once the fractions are converted to contain equal denominators, adding or subtracting them is straightforward. Simply add or subtract the numerators. Multiplying Fractions When multiply fractions, multiply the numerators by numerators and denominators by denominators. Multiplying Fractions When multiply fractions, multiply the numerators by numerators and denominators by denominators. In other words, multiply all numbers above the line; then multiply all numbers below the line. Multiplying Fractions When multiply fractions, multiply the numerators by numerators and denominators by denominators. In other words, multiply all numbers above the line; then multiply all numbers below the line. Cancel if possible and reduce to lowest terms. Discussion What happens to the value of a fraction when you multiply the numerator by a number? Discussion What happens to the value of a fraction when you multiply the numerator by a number? Answer: The value of the fraction increases. Discussion What happens to the value of a fraction when you multiply the denominator by a number? Discussion What happens to the value of a fraction when you multiply the denominator by a number? Answer: The value of the fraction decreases. Discussion What happens to the value of a fraction when you multiply the numerator and denominator by the same number? Discussion What happens to the value of a fraction when you multiply the numerator and denominator by the same number? Answer: The value of the fraction does not change because you have multiplied the original fraction by 1. Multiplying Fractions Dividing the denominator by a number is the same as multiplying the numerator by that number. 3 5 15 3 20 20 4 Multiplying Fractions Dividing the numerator by a number is the same as multiplying the denominator by that number. 6 6 1 4 3 12 2 Dividing Fractions To divide by a fraction, multiply by its reciprocal, and then reduce it if necessary. 1 1 3 3 3 1/ 3 1 1 Terms to Remember • fraction • numerator • denominator • proper fraction • improper fraction • mixed number The Arabic System The Arabic system is also called the decimal system. Terminology Arabic numbers The numbering system that uses numeric symbols to indicate a quantity, fractions, and decimals. Uses the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The Arabic System The decimal serves as the anchor. • Each place to the left of the decimal point signals a tenfold increase. • Each place to the right signals a tenfold decrease. Decimal Units and Values Terminology place value the location of a numeral in a string of numbers that describes the numeral’s relationship to the decimal point Terminology leading zero a zero that is placed to the left of the decimal point, in the ones place, in a number that is less than zero and is being represented by a decimal value Decimals • A decimal is a fraction in which the denominator is 10 or some multiple of 10. • Numbers written to the right of decimal point < 1. • Numbers written to the left of the decimal point > 1 Example 2 Multiply the two given fractions. Terminology decimal a fraction value in which the denominator is 10 or some multiple of 10 Remember • Numbers to the left of the decimal point are whole numbers. • Numbers to the right of the decimal point are decimal fractions (part of a whole). Decimal Places Decimals Adding or Subtracting Decimals • Place the numbers in columns so that the decimal points are aligned directly under each other. • Add or subtract from the right column to the left column. Decimals Multiplying Decimals • Multiply two decimals as whole numbers. • Add the total number of decimal places that are in the two numbers being multiplied. • Count that number of places from right to left in the answer, and insert a decimal point. Decimals Dividing Decimals 1. Change both the divisor and dividend to whole numbers by moving their decimal points the same number of places to the right. • divisor: number doing the dividing, the denominator • dividend: number being divided, the numerator 2. If the divisor and the dividend have different number of digits after the decimal point, choose the one that has more digits and move its decimal point a sufficient number of places to make it a whole number. Decimals Dividing Decimals 3. Move the decimal point in the other number the same number of places, adding zeros at the end if necessary. 4. Move the decimal point in the dividend the same number of places, adding a zero at the end. Decimals Dividing Decimals 1.45 ÷ 3.625 = 0.4 1.45 1450 0 .4 3.625 3625 Decimals Rounding Decimals • Rounding numbers is essential for accuracy. • It may not be possible to measure a very small quantity such as a hundredth of a milliliter. • A volumetric dose is commonly rounded to the nearest tenth. • A solid dose is commonly rounded to the hundredth or thousandth place, pending the accuracy of the measuring device. Decimals Rounding to the Nearest Tenth 1. Carry the division out to the hundredth place 2. If the hundredth place number ≥ 5, + 1 to the tenth place 3. If the hundredth place number ≤ 5, round the number down by omitting the digit in the hundredth place 5.65 becomes 5.7 4.24 becomes 4.2 Decimals Rounding to the Nearest Hundredth or Thousandth Place 3.8421 = 3.84 41.2674 = 41.27 0.3928 = 0.393 4.1111 = 4.111 Decimals Rounding the exact dose 0.08752 g . . . to the nearest tenth: 0.1 g . . . to he nearest hundredth: 0.09 g . . . to the nearest thousandth: 0.088 g Discussion When a number that has been rounded to the tenth place is multiplied or divided by a number that was rounded to the hundredth or thousandth place, the resultant answer must be rounded back to the tenth place. Why? Discussion When a number that has been rounded to the tenth place is multiplied or divided by a number that was rounded to the hundredth or thousandth place, the resultant answer must be rounded back to the tenth place. Why? Answer: The answer can only be accurate to the place to which the highest rounding was made in the original numbers. Decimals • In most cases, a zero occurring at the end of a digits is not written. • Do not drop the zero when the last digit resulting from rounding is a zero. Such a zero is considered significant to that particular problem or dosage. Numerical Ratios Ratios represent the relationship between • two parts of the whole • one part to the whole Numerical Ratios Written with as follows: 1:2 3:4 “1 part to 2 parts” “3 parts to 4 parts” ½ ¾ Can use “per,” “in,” or “of,” instead of “to” Terminology ratio a numerical representation of the relationship between two parts of the whole or between one part and the whole Numerical Ratios in the Pharmacy 1:100 concentration of a drug means . . . Numerical Ratios in the Pharmacy 1:100 concentration of a drug means . . . . . . there is 1 part drug in 100 parts solution Proportions • An expression of equality between two ratios. • Noted by :: or = 3:4 = 15:20 or 3:4 :: 15:20 Terminology proportion an expression of equality between two ratios Proportions If a proportion is true . . . product of means = product of extremes 3:4 = 15:20 3 × 20 = 4 × 15 60 = 60 Proportions product of means = product of extremes a:b = c:d b×c=a×d Proportions in the Pharmacy • Proportions are frequently used to calculate drug doses in the pharmacy. • Use the ratio-proportion method any time one ratio is complete and the other is missing a component. Terminology ratio-proportion method a conversion method based on comparing a complete ratio to a ratio with a missing component Rules for Ratio-Proportion Method • Three of the four amounts must be known. • The numerators must have the same unit of measure. • The denominators must have the same unit of measure. Steps for solving for x 1. Calculate the proportion by placing the ratios in fraction form so that the x is in the upperleft corner. Steps for solving for x 1. Calculate the proportion by placing the ratios in fraction form so that the x is in the upper-left corner. 2. Check that the unit of measurement in the numerators is the same and the unit of measurement in the denominators is the same. Steps for solving for x 1. Calculate the proportion by placing the ratios in fraction form so that the x is in the upper-left corner. 2. Check that the unit of measurement in the numerators is the same and the unit of measurement in the denominators is the same. 3. Solve for x by multiplying both sides of the proportion by the denominator of the ratio containing the unknown, and cancel. Steps for solving for x 1. Calculate the proportion by placing the ratios in fraction form so that the x is in the upper-left corner. 2. Check that the unit of measurement in the numerators is the same and the unit of measurement in the denominators is the same. 3. Solve for x by multiplying both sides of the proportion by the denominator of the ratio containing the unknown, and cancel. 4. Check your answer by seeing if the product of the means equals the product of the extremes. Remember When setting up a proportion to solve a conversion, the units in the numerators must match, and the units in the denominators must match. Example 3 Solve for x. Example 3 Solve for x. Example 3 Solve for x. Percents • Percent means “per 100” or hundredths. • Represented by symbol % 30% = 30 parts in total of 100 parts, 30 30:100, 0.30, or 100 Terminology percent the number of parts per 100; can be written as a fraction, a decimal, or a ratio Discussion If you take a test with 100 questions, and you get a score of 89%, how many questions did you get correct? Discussion If you take a test with 100 questions, and you get a score of 89%, how many questions did you get correct? Answer: 89 89:100, 89/100, or 0.89 Percents in the Pharmacy • Percent strengths are used to describe IV solutions and topically applied drugs. • The higher the % of dissolved substances, the greater the strength. Percents in the Pharmacy A 1% solution contains . . . • 1 g of drug per 100 mL of fluid • Expressed as 1:100, 1/100, or 0.01 Percents in the Pharmacy A 1% hydrocortisone cream contains . . . • 1 g of hydrocortisone per 100 g of cream • Expressed as 1:100, 1/100, or 0.01 Safety Note! The higher the percentage of a dissolved substance, the greater the strength. Percents in the Pharmacy • Multiply the first number in the ratio (the solute) while keeping the second number unchanged, you increase the strength. • Divide the first number in the ration while keeping the second number unchanged, you decrease the strength. Equivalent Values Percent Fraction Decimal Ratio 45% 45 100 0.45 45:100 0.5% 0.5 100 0.005 0.5:100 Converting a Ratio to a Percent 1. Designate the first number of the ratio as the numerator and the second number as the denominator. 2. Multiply the fraction by 100%, and simply as needed. Remember Multiplying a number or a fraction by 100% does not change the value. Converting a Ratio to a Percent 5:1 = 5/1 × 100% = 5 × 100% = 500% 1:5 = 1/5 × 100% = 100%/5 = 20% 1:2 = 1/2 × 100% = 100%/2 = 50% Converting a Percent to a Ratio 1. Change the percent to a fraction by dividing it by 100. Converting a Percent to a Ratio 1. Change the percent to a fraction by dividing it by 100. 2. Reduce the fraction to its lowest terms. Converting a Percent to a Ratio 1. Change the percent to a fraction by dividing it by 100. 2. Reduce the fraction to its lowest terms. 3. Express this as a ratio by making the numerator the first number of the ratio and the denominator the second number. Converting a Percent to a Ratio 2% = 2 ÷ 100 = 2/100 = 1/50 = 1:50 10% = 10 ÷ 100 = 10/100 = 1/10 = 1:10 75% = 75 ÷ 100 = 75/100 = 3/4 = 3:4 Converting a Percent to a Decimal 1. Divide by 100% or insert a decimal point two places to the left of the last number, inserting zeros if necessary. 2. Drop the % symbol. Remember Multiplying or dividing by 100% does not change the value because 100% = 1. Converting a Decimal to a Percent 1. Multiply by 100% or insert a decimal point two places to the right of the last number, inserting zeros if necessary. 2. Add the the % symbol. Percent to Decimal 4% = 0.04 4 ÷ 100% = 0.04 15% = 0.15 15 ÷ 100% = 0.15 200% = 2 200 ÷ 100% = 2 Decimal to Percent 0.25 = 25% 0.25 × 100% = 25% 1.35 = 135% 1.35 × 100% = 135% 0.015 = 1.5% 0.015 × 100% = 1.5% Terms to Remember • common denominator • least common denominator • decimal • leading zero • ratio • proportion • percent COMMON CALCULATIONS IN THE PHARMACY • Converting Quantities between the Metric and Common Measure Systems • Calculations of Doses • Preparation of Solutions COMMON CALCULATIONS IN THE PHARMACY • Converting Quantities between the Metric and Common Measure Systems Example 4 How many milliliters are there in 1 gal, 12 fl oz? According to the values in Table 5.7, 3840 mL are found in 1 gal. Because 1 fl oz contains 30 mL, you can use the ratio-proportion method to calculate the amount of milliliters in 12 fl oz as follows: Example 4 How many milliliters are there in 1 gal, 12 fl oz? Example 4 How many milliliters are there in 1 gal, 12 fl oz? Example 4 How many milliliters are there in 1 gal, 12 fl oz? Example 5 A solution is to be used to fill hypodermic syringes, each containing 60 mL, and 3 L of the solution is available. How many hypodermic syringes can be filled with the 3 L of solution? From Table 5.2, 1 L is 1000 mL. The available supply of solution is therefore Example 5 How many hypodermic syringes can be filled with the 3 L of solution? Determine the number of syringes by using the ratio-proportion method: Example 5 How many hypodermic syringes can be filled with the 3 L of solution? Example 5 How many hypodermic syringes can be filled with the 3 L of solution? Example 6 You are to dispense 300 mL of a liquid preparation. If the dose is 2 tsp, how many doses will there be in the final preparation? Begin solving this problem by converting to a common unit of measure using conversion values in Table 5.7. Example 6 If the dose is 2 tsp, how many doses will there be in the final preparation? Using these converted measurements, the solution can be determined one of two ways. Solution 1: Using the ratio proportion method and the metric system, Example 6 If the dose is 2 tsp, how many doses will there be in the final preparation? Example 6 If the dose is 2 tsp, how many doses will there be in the final preparation? Example 7 How many grains of acetaminophen should be used in a Rx for 400 mg acetaminophen? Solve this problem by using the ratio-proportion method. The unknown number of grains and the requested number of milligrams go on the left side, and the ratio of 1 gr 65 mg goes on the right side, per Table 5.5. Example 7 How many grains of acetaminophen should be used in the prescription? Example 7 How many grains of acetaminophen should be used in the prescription? Example 8 A physician wants a patient to be given 0.8 mg of nitroglycerin. On hand are tablets containing nitroglycerin 1/150 gr. How many tablets should the patient be given? Begin solving this problem by determining the number of grains in a dose by setting up a proportion and solving for the unknown. Example 8 How many tablets should the patient be given? Example 8 How many tablets should the patient be given? Example 8 How many tablets should the patient be given? Example 8 How many tablets should the patient be given? Example 8 How many tablets should the patient be given? COMMON CALCULATIONS IN THE PHARMACY • Calculations of Doses active ingredient (to be administered)/solution (needed) = active ingredient (available)/solution (available Measurement and Calculation Issues Safety Note! Always double-check the units in a proportion and doublecheck your calculations. Example 9 You have a stock solution that contains 10 mg of active ingredient per 5 mL of solution. The physician orders a dose of 4 mg. How many milliliters of the stock solution will have to be administered? Example 9 How many milliliters of the stock solution will have to be administered? Example 9 How many milliliters of the stock solution will have to be administered? Example 10 An order calls for Demerol 75 mg IM q4h prn pain. The supply available is in Demerol 100 mg/mL syringes. How many milliliters will the nurse give for one injection? Example 10 How many milliliters will the nurse give for one injection? Example 10 How many milliliters will the nurse give for one injection? Example 11 An average adult has a BSA of 1.72 m2 and requires an adult dose of 12 mg of a given medication. If the child has a BSA of 0.60 m2, and if the proper dose for pediatric and adult patients is a linear function of the BSA, what is the proper pediatric dose? Round off the final answer. Example 11 What is the proper pediatric dose? Example 11 What is the proper pediatric dose? Example 11 What is the proper pediatric dose? Example 11 What is the proper pediatric dose? COMMON CALCULATIONS IN THE PHARMACY • Preparation of Solutions powder volume = final volume – diluent volume Example 12 A dry powder antibiotic must be reconstituted for use. The label states that the dry powder occupies 0.5 mL. Using the formula for solving for powder volume, determine the diluent volume (the amount of solvent added). You are given the final volume for three different examples with the same powder volume. Example 12 Using the formula for solving for powder volume, determine the diluent volume. Example 12 Using the formula for solving for powder volume, determine the diluent volume. Example 13 You are to reconstitute 1 g of dry powder. The label states that you are to add 9.3 mL of diluent to make a final solution of 100 mg/mL. What is the powder volume? Example 13 What is the powder volume? Step 1. Calculate the final volume. The strength of the final solution will be 100 mg/mL. Example 13 What is the powder volume? Example 13 What is the powder volume? Example 13 What is the powder volume? Measurement and Calculation Issues Safety Note! An injected dose generally has a volume greater than 0.1 mL and less than 1 mL. Example 14 Dexamethasone is available as a 4 mg/mL preparation; an infant is to receive 0.35 mg. Prepare a dilution so that the final concentration is 1 mg/mL. How much diluent will you need if the original product is in a 1 mL vial and you dilute the entire vial? Example 14 How much diluent will you need if the original product is in a 1 mL vial and you dilute the entire vial? Example 14 How much diluent will you need if the original product is in a 1 mL vial and you dilute the entire vial? Example 14 How much diluent will you need if the original product is in a 1 mL vial and you dilute the entire vial? Example 15 Prepare 250 mL of dextrose 7.5% weight in volume (w/v) using dextrose 5% (D5W) w/v and dextrose 50% (D50W) w/v. How many milliliters of each will be needed? Example 15 How many milliliters of each will be needed? Step 1. Set up a box arrangement and at the upper-left corner, write the percent of the highest concentration (50%) as a whole number. Example 15 How many milliliters of each will be needed? Step 2. Subtract the center number from the upper-left number (i.e., the smaller from the larger) and put it at the lower-right corner. Now subtract the lower-left number from the center number (i.e., the smaller from the larger), and put it at the upper-right corner. Example 15 How many milliliters of each will be needed? Example 15 How many milliliters of each will be needed? Example 15 How many milliliters of each will be needed? Example 15 How many milliliters of each will be needed? Example 15 How many milliliters of each will be needed? Example 15 How many milliliters of each will be needed? Example 15 How many milliliters of each will be needed? Example 15 How many milliliters of each will be needed? Example 15 How many milliliters of each will be needed? Example 15 How many milliliters of each will be needed? Example 15 How many milliliters of each will be needed? Terms to Remember • power volume (pv) • alligation Discussion Visit www.malpracticeweb.com, and look under Miscellaneous to find legal summaries of the following cases. Describe the decision and explain how this decision affects pharmacy technicians. a. J.C. vs. Osco Drug b. P.H. vs. Osco Drug Discussion What activities of the pharmacy technician require skill in calculations?