Summarize metric notation.
Calculate equivalent measurements within the metric system.
Identify the most frequently used equivalent measurements among metric, household, and apothecaries’ measurements.
Convert measurements between the metric, household, and apothecary systems of measurement.

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Math for the Pharmacy Technician: Concepts and CalculationsChapter 3: Systems of Measurement and WeightEgler • BoothSystems of Weights and Measures2Learning ObjectivesSummarize metric notation.Calculate equivalent measurements within the metric system.Identify the most frequently used equivalent measurements among metric, household, and apothecaries’ measurements.Convert measurements between the metric, household, and apothecary systems of measurement.When you have successfully completed Chapter 3, you will have mastered skills to be able to:3Learning Objectives (con’t)List the fundamental units of the metric system for length, weight, and volume.Recognize the symbols for dram, ounce, grain, and drop. Calculate temperature and time conversions.4IntroductionLarge numbers of medications are measured in grams and milligrams (units of the metric system).Understanding and converting systems of weights and measures are required of pharmacy technicians.5Metric SystemWidely used system of measurement in the world today.Defined in 1792, gets its name from the meter (basic unit of length).A meter is about three inches longer than a yard.See next slide for Table 3-1 “Basic Units of Metric Measurement.”6Table 3-1 Basic Units of Metric Measurement7Metric System (con’t)Meter and gram are abbreviated with lowercase letters.Liter is abbreviated with an uppercase L.This minimizes the chance of confusion between 1 and the lowercase L.8Metric System (con’t)Length used for measurement such as patient height.Weight and volume are used to calculate medications dosages.9Understanding Metric NotationMetric system is based on multiples of 10.Prefix before the basic unit indicates size.Kilo – indicates you multiply the basic unit by 1000.Kilometer – 1000 metersKilogram – 1000 gramsKiloliter – 1000 litersWhen you divide a meter by 1000 equal lengths, each length is one millimeter.10Understanding Metric Notation (con’t)Prefix milli- means one-thousandth.Millimeter is one-thousandth of a meter.Milliliter is one-thousandth of a liter.Milligram is one-thousandth of a gram.See Tables 3-2 and 3-3 in your textbook to visualize these concepts.11Kilo – prefix indicates basic unit times 1000Micro – indicates of basic unitMetric System TermsGram – measure unit of weightLiter – unit of volumeMeter – unit of lengthCenti- indicates of the basic unit12Basic Units of Metric MeasurementType of MeasureBasic Unit AbbreviationLengthmetermWeight (or Mass)gramgVolumeliterL13Common Metric System PrefixesPrefixLengthValuekilo- (k)kilometer (km)1 km = 1000 m(basic unit)meter (m) 1 mcenti- (c)centimeter (cm)1 cm = = 0.01 m14Common Metric System Prefixes (con’t)PrefixLengthValuemilli- (m)millimeter (mm)1 mm = 0.001 mmicro- (mc or μ )micrometer (mcm) 1 mcm = == 0.00000115Combining Prefixes and Units (con’t)PrefixWeight (Mass)(gram)Volume (liter)kilo-(x1000) kilometerkmkilogramkgkiloliterkLcenti-(100) centimetercmcentigramcgcentilitercLmilli-(1000) millimetermmmilligrammgmillilitermLmicro-( 1,000,000)micrometer mcmmicrogram mcgmicrolitermcLLength (meter)16Understanding Metric Notation Use Arabic numerals, with decimals to represent any fractions.For example: Write 1.25 g to represent 1 1/4 g If the quantity is less than 1, include a 0 before the decimal point. Delete any other zeros that are not necessary.For example: Do not write .750; write 0.75, adding a zero before the decimal point and deleting the unnecessary zero at the end.17Understanding Metric Notation (con’t) Write the unit after the quantity with a space between them.For example: Write 30 mg, not mg 30. 18 Use lowercase letters for metric abbreviations. However, use uppercase L to represent liter.For example: Write mg, not M.For example: Write mL, not ml. Understanding Metric Notation (con’t)19Determine the correct metric notation for six and two-eighths milliliters.a. 6.28mLb. ml 6.25c. 6 mLd. 6.25 mLReview and PracticeAnswer d. 6.25 mL20Converting within the Metric System To convert a quantity from one unit of metric measurement to another:1. Move the decimal point to the right if you are converting from a larger unit to a smaller unit.2. Move the decimal point to the left if you are converting from a smaller unit to a larger unit.21Review and Practice1. Convert 4 L to mL. 4 L = 4.000 L = 4000 mL75 mm = 75.0 mm = 0.075 m2. How many m are in 75 mm?22CAUTIONRemember: The larger the unit, the smaller the quantity. The smaller the unit, the larger the quantity.For example: 1 dollar bill = 4 quarters = 100 penniesFor example: 100 pennies = 4 quarters = 1 dollar bill23Apothecary SystemAn old system of measurementFirst used by apothecaries (early pharmacists) and moved from Europe to colonial America.Household system evolved from the apothecary system.Very few medications are still measured in apothecary units.24Dram ( ) – common unit of volume in the apothecaryGrain – basic unit Minim ( ) – common unit of volumeOunce ( ) – fluid ounces of volumeUnit (USP Unit) – amount of medication to produce an effectApothecary System Terms25Apothecary SystemCAUTION!Do not confuse grains and grams.grains (gr)grams (g)1 gr = 60 mg = 0.06 g OR1 gr = 65 mg = 0.065 gThe basic unit of weight is the grain (gr).26The three common units of volume areminim ( )dram ( )ounce ( )Apothecary System (con’t)CAUTION!Do not confuse the symbols for drams and ounces.1 ounce ( ) = 8 drams ( )27Apothecary SystemApothecary ounce is used in the United States.8 ounces to a cup is commonly used in the home to measure liquids.The dram is most frequently used to abbreviate teaspoonful which is nearly the same volume.28Apothecary NotationWhen writing a value in the apothecary system:1. If a value is less than 1, write it as a fraction. However, if the value is one-half, write it as the abbreviation ss.2. Write the values with lowercase Roman numerals. 293. Use the abbreviation gr to represent grain. Use the symbols ( ), ( ), and ( ) to represent minim, dram, and ounce.Apothecary Notation (cont.)4. Write the abbreviation, symbol or unit before the quantity.301. Write four grains using apothecary notation.2. Write two and one-half grains using apothecary notation.Review and Practicegr iv or gr ivgr iiss xiiWrite twelve ounces using apothecary notation.31Apothecary and Household EquivalentsUnits of measurement found in the apothecary and the household systems are equalApothecary ounces = household ouncesNeither system is based on multiples of 1032Abbreviations for Household MeasuresUnit of MeasurementAbbreviationsdropgt or gtt (plural)teaspoontsp or ttablespoon tbs or Tounce oz or 33Abbreviations for Household Measures (con’t)Unit of MeasurementAbbreviationcupcup (c)pintptquartqtgallongal34Review and PracticeWrite the quantity in Arabic numerals before the abbreviation for the unit.Example: Write six drops using household notation.6 gttExample: Write twelve ounces using household notation.12 oz35Apothecary and Household Equivalent Measuresdrop1 drop = 1 minimteaspoon1 teaspoon = 60 dropstablespoon1 tablespoon = 3 teaspoonsounce1 ounce= 2 tablespoonscup1 cup =8 ounces36Review and PracticeHow many teaspoons of solution are contained in 1 ounce of solution?1 oz = 2 x 1 tbs = 2 x 3 tsp = 6 tspHow many tablespoons are in ½ cup?½ cup = ½ x 1 cup = ½ x 8 oz = 4 oz = 4 x 1 oz = 4 x 2 tbs = 8 tbs37Milliequivalents and UnitsMilliequivalents (mEq)The mEq is defined as of an equivalent weight of a chemical.Sodium and potassium are often measured in mEq.USP Units (U)Medications such as insulin, heparin, and penicillin are measured in units (U).Size of the unit varies for each drug.38Converting Among Metric, Apothecary, and Household SystemsWhen calculating drug dosages, you must often convert among the metric, apothecary, and household systems.You need to know how the measure of a quantity in one system compares to its measure in another system.1 tsp = 5 mL = 5 cc39Equivalent Volume MeasurementsMetricHouseholdApothecary5 mL1 tsp1 dr15 mL1 tbs3 or 4 dr30 mL2 tbs = 1 oz1 oz40Equivalent Volume Measurements (con’t)MetricHouseholdApothecary240 mL8 oz = 1 c8 oz480 mL2 c = 1 pt16 oz960 mL2 pt = 1 qt32 oz41Table 3-8 Equivalent Weight MeasurementsMetricApothecary60 mggr i (1 grain)30 mggr ss ( grain)15 mggr1 mggr42Table 3-8 Equivalent Weight Measurements (con’t)MetricApothecary1 g (1000mg)gr xv (15 grains)0.5 ggr viiss (7 grains)1 kg2.2 lb43Conversion FactorsConversion factor is a fraction made of two quantities that are equal to one another but which are expressed in different units. Refer back to Table 3-8. 1 kg and 2.2 lb are equalTwo different conversion factors can be formed. 1 kg/2.2 lb and 2.2 lb/1 kg44Using Conversion FactorsWhen writing a conversion factor:The two quantities in the conversion factor must be equal to one another.The quantity containing the units that you wish to convert to goes in the numerator of the conversion factor.The quantity containing the units that you are converting from goes in the denominator of the conversion factor.45Using Conversion Factors (con’t)ExampleWrite a conversion factor for converting from milliliters to ouncesPut ounces as the numeratorThe correct conversion factor is 46Using Conversion Factors:Fraction Proportion MethodProcedure Checklist 3-1: Converting by the Fraction Proportion MethodWrite a conversion factor with the units that you are converting to in the numerator and the units you are converting from in the denominator.Write a fraction with the unknown, “?”.47Using Conversion Factors:Fraction Proportion MethodProcedure Checklist (con’t)3-1: Converting by the Fraction Proportion MethodSet the two fractions up as a proportion.Cancel units.Cross-multiply, then solve for the unknown value.48Review and PracticeHow many kg does a 62-pound child weigh?62 lb = 2.2 lb? kg 1 kg 62 x 1 = ? x 2.262 = 2.2 x ?28.18 = ?49Using Conversion Factors:Ratio Proportion MethodProcedure Checklist 3-2: Converting by the Ratio Proportion MethodWrite a conversion factor as a ratio A:B so that A has the units of the value that you are converting.Write the second C:D so that C is the missing value and D is the number that is being converted. 50Using Conversion Factors:Ratio Proportion MethodProcedure Checklist (con’t)3-2: Converting by the Ratio Proportion MethodWrite the proportion in the form A:B::C:D.Cancel units.Solve the proportion by multiplying means and extremes.51Review and PracticeHow many kg does a 66-pound child weigh?1 kg = 2.2 lbFirst ratio is 1 kg:2.2 lbSecond ratio is ?:661 kg:2.2::?:66Solve for missing value?=30 kg52Using Conversion Factors:Dimensional AnalysisProcedure Checklist 3-3: Converting using the Dimensional Analysis MethodDetermine the unit of measure for the answer and place it as the unknown on one side of the equation.On the other side of the equation, write a conversion factor with the units of measure for the answer on top and the units you are converting from on the bottom.53Using Conversion Factors: Dimensional AnalysisProcedure Checklist (con’t)3-3: Converting using the Dimensional Analysis MethodMultiply the numerator of the conversion factor by the number that is being converted.Cancel units on the right side of the equation. The remaining unit of measure on the right side of the equation should match the unknown unit of measure on the left side of the equation.Solve the equation.54Review and PracticeConvert 66 lb into kilograms.1 kg = 2.2 lb?/kg=1 kg/2.2 lb?kg = 66 lb x 1 kg 2.2 lb? = 30 kg55Review and PracticeYou are instructing a patient to take 10 mL of medication at home, using a calibrated teaspoon to measure the medication. How many teaspoons should the patient use?10 mL:? tsp::5 mL:1 tsp? x 5 = 10 x 15 x ? = 10? = 256Review and PracticeConvert the measures from one system of measurement to another.Answer = 180 mLAnswer = 22.5 mL 6 oz = ? mLYour patient is to receive 1.5 tbsof medicated mouthwash. How many cc of medicated mouthwash should the patient receive?57TemperatureBoth Fahrenheit (F) and Celsius (C) temperature scales are used in health-care settings.Celsius temperature is also known as Centigrade (C) temperature scale.Water freezes at 32 degrees Fahrenheit 0 degrees Centigrade58Temperature (con’t)Water boils at212 degrees Fahrenheit100 degrees CelsiusConverting between these two temperature scales is sometimes necessary.Use formulas to convert between the systems.59Temperature (con’t)Converting Between Temperature SystemsTo convert from F to C use:°F- 32 = °C 1.8To convert from C to F use:(1.8 X °C) + 32 = °F60Temperature (con’t)Converting Between Temperature SystemsYou can also use the formula 5F-160 = 9C to convert between Fahrenheit and Celsius.61Review and PracticeConvert the temperatures.Answer = 95 0FAnswer = 39.8 0C 35 0C = ? 0F 103.6 0F = ? 0C62TimeTraditional 12-hour clockIt can be a source of errors in medication administration.Each time occurs twice daily.10:00 a.m.10:00 p.m.63Time (con’t)24-hour clockMilitary or international timeEach time occurs only once per day10:00 a.m. = 100010:00 p.m. = 220064Time (con’t)When using a 24-hour clock for international time: Write 00 as the first two digits to represent the first hour after midnight.2. Write 01, 02, 03, 09 as the first two digits to represent the hours 1:00 a.m. through 9:00 a.m.65Time (con’t) 3. Add 12 to the first two digits to represent the hours 12:00 p.m. through 11:00 p.m. so that 12, 13, 14, 23 represent these hours.4. Write midnight as either 2400 (international) or 0000 (military time).66Review and PracticeConvert 9:00 a.m. to international time.9:00 a.m. = 0900Convert 12:19 a.m. to international time.12:19 a.m. = 0019Convert 4:28 p.m. to international time.4:28 p.m. = 162867Review and Practice (con’t)Convert 1139 to traditional time.1139 = 11:39 a.m.Convert 1515 to traditional time.1515 = 3:15 p.m.68International TimeTo state the time using international time:Say “zero” if the first digit is a zero.Say “zero zero” if the first two digits are both zero.If the minutes are represented by 00, then say “hundred” after you say the hour.69Review and PracticeState the time 0900.*Say “zero nine hundred.” State the time 1139.*Say “eleven thirty-nine.”State the time 0023.*Say “ zero zero twenty-three.”70Review and PracticeConvert 5.0 mcg to mg.5.0 mcg ÷ 1000 = 0.005 mgConvert 43 kg to g.43 x 1000 = 43,000 g71Review and PracticeHow many kg does an 88-pound child weigh?88 lb = 2.2 lb ? kg 1 kg 88 x 1 = ? x 2.288 = 2.2 x ?40 kg = ?72Review and PracticeConvert 50ºC to ºF.(1.8 x 50) + 32 = ºF(90) + 32 = ºF122 = ºFConvert 100ºF to ºC.73Systems of Weights and MeasuresTHE ENDAs a pharmacy technician it is imperative that you master the concepts of the systems of measurements and weights. You need to be able to “measure up to the mark,” so to speak, as you will use units of measurement and weight in all dosage calculations.74