Math for the Pharmacy Technician: Concepts and Calculations

1. Math for the Pharmacy Technician: Concepts and Calculations Egler • Booth Chapter 3: Systems of Measurement and Weight

2. Systems of Weights and Measures

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:

4. LearningObjectives (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 temperatureand time conversions.

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.

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.”

7. Table 3-1 Basic Units of Metric Measurement

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.

9. Metric System (con’t) • Length used for measurement such as patient height. • Weight and volume are used to calculate medications dosages.

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.

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.

12. Metric System Terms • Gram – measure unit of weight • Liter – unit of volume • Meter – unit of length • Centi- indicates of the basic unit • Kilo – prefix indicates basic unit times 1000 • Micro – indicates of basic unit

13. Basic Units of Metric Measurement

14. Common Metric System Prefixes

15. Common Metric System Prefixes (con’t)

16. Prefix Length (meter) Weight (Mass) (gram) Volume (liter) Combining Prefixes and Units (con’t) 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 mcg microliter mcL

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.

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.

19. Understanding Metric Notation (con’t) 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.

20. Answer d. 6.25 mL Review and Practice • 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

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.

22. Review and Practice 1. Convert 4 L to mL. 4 L = 4.000 L = 4000 mL 2. How many m are in 75 mm? 75 mm = 75.0 mm = 0.075 m

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

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.

25. Apothecary System Terms • 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

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).

27. Apothecary System (con’t) • The three common units of volume are • minim ( ) • dram ( ) • ounce ( ) CAUTION! • Do not confuse the symbols for drams and ounces. • 1 ounce ( ) = 8 drams ( )

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.

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.

30. Apothecary Notation (cont.) 3. Use the abbreviation gr to represent grain. Use the symbols ( ), ( ), and ( ) to represent minim, dram, and ounce. 4. Write the abbreviation, symbol or unit before the quantity.

31. gr iv or gr iv xii Review and Practice 1. Write four grains using apothecary notation. 2. Write two and one-half grains using apothecary notation. gr iiss Write twelve ounces using apothecary notation.

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

33. Abbreviations for Household Measures

34. Unit of Measurement Abbreviation cup cup (c) pint pt quart qt gallon gal Abbreviations for Household Measures (con’t)

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

36. drop 1 drop = 1 minim teaspoon 1 teaspoon = 60 drops tablespoon 1 tablespoon = 3 teaspoons ounce 1 ounce = 2 tablespoons cup 1 cup = 8 ounces Apothecary and Household Equivalent Measures

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

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) • Medications such as insulin, heparin, and penicillin are measured in units (U). • Size of the unit varies for each drug.

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

40. Equivalent Volume Measurements

41. Equivalent Volume Measurements (con’t)

42. Metric Apothecary 60 mg gr i (1 grain) 30 mg gr ss ( grain) 15 mg gr 1 mg gr Table 3-8 Equivalent Weight Measurements

43. Metric Apothecary 1 g (1000mg) gr xv (15 grains) 0.5 g gr viiss (7 grains) 1 kg 2.2 lb Table 3-8 Equivalent Weight Measurements (con’t)

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

45. Using Conversion Factors When 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.

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

47. Using Conversion Factors:Fraction Proportion Method Procedure Checklist 3-1: Converting by the Fraction Proportion Method 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. • Write a fraction with the unknown, “?”.

48. Using Conversion Factors:Fraction Proportion Method Procedure Checklist (con’t) 3-1: Converting by the Fraction Proportion Method Set the two fractions up as a proportion. Cancel units. Cross-multiply, then solve for the unknown value.

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 = ?

50. Using Conversion Factors:Ratio Proportion Method Procedure Checklist 3-2: Converting by the Ratio Proportion Method Write 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.