2. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved Math for the Pharmacy Technician: Concepts and Calculations Chapter 3: Systems of Measurement and Weight Egler Booth

3. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-2 Systems of Weights and Measures

4. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-3 Learning Objectives  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. When you have successfully completed Chapter 3, you will have mastered skills to be able to:

5. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-4 Learning 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.

6. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-5 Introduction  Large 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.

7. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-6 Metric System  Widely 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.”

8. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-7 Table 3-1 Basic Units of Metric Measurement

9. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-8 Metric 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.

10. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-9 Metric System (con’t)  Length used for measurement such as patient height.  Weight and volume are used to calculate medications dosages.

11. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-10 Understanding Metric Notation  Metric 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 meters Kilogram – 1000 grams Kiloliter – 1000 liters  When you divide a meter by 1000 equal lengths, each length is one millimeter.

12. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-11 Understanding 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.

13. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-12  Kilo – prefix indicates basic unit times 1000  Micro – indicates of basic unit Metric System Terms  Gram – measure unit of weight  Liter – unit of volume  Meter – unit of length  Centi- indicates of the basic unit

14. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-13 Basic Units of Metric Measurement Type of Measure Basic UnitAbbreviation Lengthmeterm Weight (or Mass) gramg VolumeliterL

15. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-14 Common Metric System Prefixes PrefixLengthValue kilo- (k)kilometer (km) 1 km = 1000 m (basic unit)meter (m)1 m centi- (c)centimeter (cm) 1 cm = = 0.01 m

16. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-15 Common Metric System Prefixes (con’t) PrefixLengthValue milli- (m)millimeter (mm) 1 mm = 0.001 m micro- (mc or μ ) micrometer (mcm) 1 mcm = = = 0.000001

17. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-16 Combining Prefixes and Units (con’t) PrefixWeight (Mass) (gram) Volume (liter) kilo-(x1000) kilometer km kilogram kg kiloliter kL centi-(  100) centimeter cm centigram cg centiliter cL milli-(  1000) millimeter mm milligram mg milliliter mL micro- (  1,000,000) micrometer mcm microgram mcgmicroliter mcL Length (meter)

18. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-17 Understanding 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.

19. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-18 Understanding Metric Notation (con’t) Write the unit after the quantity with a space between them. For example: Write 30 mg, not mg 30.

20. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-19 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)

21. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-20  Determine the correct metric notation for six and two-eighths milliliters. a. 6.28mL b. ml 6.25 c. 6 mL d. 6.25 mL Review and Practice Answer d. 6.25 mL

22. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-21 Converting 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.

23. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-22 Review and Practice 1. Convert 4 L to mL. 4 L = 4.000 L = 4000 mL 75 mm = 75.0 mm = 0.075 m 2. How many m are in 75 mm?

24. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-23 CAUTION  Remember: The larger the unit, the smaller the quantity. The smaller the unit, the larger the quantity. For example: 1 dollar bill = 4 quarters = 100 pennies For example: 100 pennies = 4 quarters = 1 dollar bill

25. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-24 Apothecary System  An old system of measurement  First 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.

26. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-25  Dram ( ) – common unit of volume in the apothecary  Grain – basic unit  Minim ( ) – common unit of volume  Ounce ( ) – fluid ounces of volume  Unit (USP Unit) – amount of medication to produce an effect Apothecary System Terms

27. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-26 Apothecary System CAUTION! Do not confuse grains and grams.  grains (gr)  grams (g) 1 gr = 60 mg = 0.06 g OR 1 gr = 65 mg = 0.065 g  The basic unit of weight is the grain (gr).

28. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-27  The three common units of volume are minim ( ) dram ( ) ounce ( ) Apothecary System (con’t) CAUTION! Do not confuse the symbols for drams and ounces. 1 ounce ( ) = 8 drams ( )

29. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-28 Apothecary System  Apothecary 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.

30. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-29 Apothecary Notation When 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.

31. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-30 3. 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.

32. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-31 1. Write four grains using apothecary notation. 2. Write two and one-half grains using apothecary notation. Review and Practice gr iv or gr iv gr iiss xii xii 3.Write twelve ounces using apothecary notation.

33. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-32 Apothecary and Household Equivalents  Units of measurement found in the apothecary and the household systems are equal  Apothecary ounces = household ounces  Neither system is based on multiples of 10

34. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-33 Abbreviations for Household Measures Unit of Measurement Abbreviations dropgt or gtt (plural) teaspoontsp or t tablespoontbs or T ounceoz or

35. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-34 Abbreviations for Household Measures (con’t) Unit of Measurement Abbreviation cupcup (c) pintpt quartqt gallongal

36. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-35 Review and Practice Write the quantity in Arabic numerals before the abbreviation for the unit.  Example: Write six drops using household notation. 6 gtt  Example: Write twelve ounces using household notation. 12 oz

37. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-36 Apothecary and Household Equivalent Measures drop1 drop=1 minim teaspoon1 teaspoon=60 drops tablespoon1 tablespoon=3 teaspoons ounce1 ounce=2 tablespoons cup1 cup=8 ounces

38. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-37 Review and Practice How many teaspoons of solution are contained in 1 ounce of solution? 1 oz = 2 x 1 tbs = 2 x 3 tsp = 6 tsp How 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 tbs

39. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-38 Milliequivalents and Units  Milliequivalents (mEq) The mEq is defined as of an equivalent weight of a chemical. Sodium and potassium are often measured in mEq.  USP Units (U) Medi cations such as insulin, heparin, and penicillin are measured in units (U). Size of the unit varies for each drug.

40. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-39 Converting Among Metric, Apothecary, and Household Systems  When 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 cc

41. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-40 Equivalent Volume Measurements MetricHouseholdApothecary 5 mL1 tsp1 dr 15 mL1 tbs3 or 4 dr 30 mL2 tbs = 1 oz1 oz

42. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-41 Equivalent Volume Measurements (con’t) MetricHouseholdApothecary 240 mL8 oz = 1 c8 oz 480 mL2 c = 1 pt16 oz 960 mL2 pt = 1 qt32 oz

43. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-42 Table 3-8 Equivalent Weight Measurements MetricApothecary 60 mggr i (1 grain) 30 mggr ss ( grain) 15 mggr 1 mggr

44. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-43 Table 3-8 Equivalent Weight Measurements (con’t) MetricApothecary 1 g (1000mg)gr xv (15 grains) 0.5 ggr viiss (7 grains) 1 kg2.2 lb

45. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-44 Conversion Factors  Conversion 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 equal  Two different conversion factors can be formed. 1 kg/2.2 lb and 2.2 lb/1 kg

46. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-45 Using Conversion Factors When writing a conversion factor: 1.The two quantities in the conversion factor must be equal to one another. 2.The quantity containing the units that you wish to convert to goes in the numerator of the conversion factor. 3.The quantity containing the units that you are converting from goes in the denominator of the conversion factor.

47. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-46 Using Conversion Factors (con’t) Example Write a conversion factor for converting from milliliters to ounces Put ounces as the numerator The correct conversion factor is

48. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-47 Using Conversion Factors: Fraction Proportion Method Procedure Checklist 3-1: Converting by the Fraction Proportion Method 1.Write a conversion factor with the units that you are converting to in the numerator and the units you are converting from in the denominator. 2.Write a fraction with the unknown, “?”.

49. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-48 Using Conversion Factors: Fraction Proportion Method Procedure Checklist (con’t) 3-1: Converting by the Fraction Proportion Method 3.Set the two fractions up as a proportion. 4.Cancel units. 5.Cross-multiply, then solve for the unknown value.

50. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-49 Review and Practice How many kg does a 62-pound child weigh? 62 lb = 2.2 lb ? kg 1 kg 62 x 1 = ? x 2.2 62 = 2.2 x ? 28.18 = ?

51. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-50 Using Conversion Factors: Ratio Proportion Method Procedure Checklist 3-2: Converting by the Ratio Proportion Method 1.Write a conversion factor as a ratio A:B so that A has the units of the value that you are converting. 2.Write the second C:D so that C is the missing value and D is the number that is being converted.

52. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-51 Using Conversion Factors: Ratio Proportion Method Procedure Checklist (con’t) 3-2: Converting by the Ratio Proportion Method 3.Write the proportion in the form A:B::C:D. 4.Cancel units. 5.Solve the proportion by multiplying means and extremes.

53. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-52 Review and Practice How many kg does a 66-pound child weigh? 1 kg = 2.2 lb First ratio is 1 kg:2.2 lb Second ratio is ?:66 1 kg:2.2::?:66 Solve for missing value ?=30 kg

54. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-53 Using Conversion Factors: Dimensional Analysis Procedure Checklist 3-3: Converting using the Dimensional Analysis Method 1.Determine the unit of measure for the answer and place it as the unknown on one side of the equation. 2.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.

55. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-54 Using Conversion Factors: Dimensional Analysis Procedure Checklist (con’t) 3-3: Converting using the Dimensional Analysis Method 3.Multiply the numerator of the conversion factor by the number that is being converted. 4.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. 5.Solve the equation.

56. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-55 Review and Practice Convert 66 lb into kilograms. 1 kg = 2.2 lb ?/kg=1 kg/2.2 lb ?kg = 66 lb x 1 kg 2.2 lb 2.2 lb ? = 30 kg

57. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-56 Review and Practice  You 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 1 5 x ? = 10 ? = 2

58. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-57 Review and Practice Convert the measures from one system of measurement to another. Answer = 180 mL Answer = 22.5 mL 6 oz = ? mL Your patient is to receive 1.5 tbs of medicated mouthwash. How many cc of medicated mouthwash should the patient receive?

59. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-58 Temperature  Both 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 Centigrade

60. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-59 Temperature (con’t)  Water boils at 212 degrees Fahrenheit 100 degrees Celsius  Converting between these two temperature scales is sometimes necessary.  Use formulas to convert between the systems.

61. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-60 Temperature (con’t) Converting Between Temperature Systems  To convert from F to C use: °F- 32 = °C 1.8  To convert from C to F use: (1.8 X °C) + 32 = °F

62. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-61 Temperature (con’t) Converting Between Temperature Systems You can also use the formula 5F-160 = 9C to convert between Fahrenheit and Celsius.

63. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-62 Review and Practice Convert the temperatures. Answer = 95 0 F Answer = 39.8 0 C 35 0 C = ? 0 F 103.6 0 F = ? 0 C

64. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-63 Time  Traditional 12-hour clock It can be a source of errors in medication administration. Each time occurs twice daily.  10:00 a.m.  10:00 p.m.

65. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-64 Time (con’t)  24-hour clock Military or international time Each time occurs only once per day  10:00 a.m. = 1000  10:00 p.m. = 2200

66. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-65 Time (con’t) When using a 24-hour clock for international time: 1.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.

67. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-66 Time (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).

68. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-67 Review and Practice Convert 9:00 a.m. to international time. 9:00 a.m. = 0900 Convert 12:19 a.m. to international time. 12:19 a.m. = 0019 Convert 4:28 p.m. to international time. 4:28 p.m. = 1628

69. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-68 Review and Practice (con’t) Convert 1139 to traditional time. 1139 = 11:39 a.m. Convert 1515 to traditional time. 1515 = 3:15 p.m.

70. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-69 International Time To state the time using international time: 1.Say “zero” if the first digit is a zero. 2.Say “zero zero” if the first two digits are both zero. 3.If the minutes are represented by 00, then say “hundred” after you say the hour.

71. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-70 Review and Practice State the time 0900.* Say “zero nine hundred.” State the time 1139.* Say “eleven thirty-nine.” State the time 0023.* Say “ zero zero twenty-three.”

72. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-71 Review and Practice Convert 5.0 mcg to mg. 5.0 mcg ÷ 1000 = 0.005 mg Convert 43 kg to g. 43 x 1000 = 43,000 g

73. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-72 Review and Practice How many kg does an 88-pound child weigh? 88 lb = 2.2 lb ? kg 1 kg 88 x 1 = ? x 2.2 88 = 2.2 x ? 40 kg = ?

74. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-73 Review and Practice Convert 50ºC to ºF. (1.8 x 50) + 32 = ºF (90) + 32 = ºF 122 = ºF Convert 100ºF to ºC.

75. McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 3-74 Systems of Weights and Measures THE END As 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.