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Math and Dosage Calculations for Health Care Third Edition Booth & Whaley

Math and Dosage Calculations for Health Care Third Edition Booth & Whaley. Chapter 3: Systems of Weights and Measures. Learning Outcomes. 3.1 List the fundamental units of the metric system for length, weight, and volume. 3.2 Summarize metric notation.

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Math and Dosage Calculations for Health Care Third Edition Booth & Whaley

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  1. Math and Dosage Calculations for Health CareThird EditionBooth & Whaley Chapter 3: Systems of Weights and Measures McGraw-Hill

  2. Learning Outcomes 3.1 List the fundamental units of the metric system for length, weight, and volume. 3.2 Summarize metric notation. 3.3 Calculate equivalent measurements within the metric system. 3.4 Recognize the symbols for dram, ounce, grain, and drop. McGraw-Hill

  3. Learning Outcomes (cont.) 3.5 Identify the most frequently used equivalent measurements among metric, household, and apothecaries’ measurements. 3.6 Convert measurements within and among the metric, household, and apothecaries’ systems of measurement. 3.7 Calculate temperature and time conversions. McGraw-Hill

  4. Introduction • Medications are most often measured in grams and milligrams (units of the metric system). • Healthcare employees must • Understand system of weights and measures • Be able to convert these systems McGraw-Hill

  5. Dosage calculation Metric System • Most widely uses system of measurement • Named for the meter (basic unit of length). • A meter = 39.37 inches • Basic units • Meter – length for measurements of height, circumference, wound size • Gram – weight • Liter - volume McGraw-Hill

  6. Basic Units of Metric Measurement Metric System (cont.) • Meter and gram are abbreviated with lowercase letters • Liter is abbreviated with an uppercase L • Minimizes the possibility of confusion between 1 and the lowercase L McGraw-Hill

  7. Understanding Metric Notation • Based on multiples of 10 • Prefix before the basic unit indicates size • Kilo –multiply the basic unit by 1000 • Kilometer – 1000 meters • Kilogram – 1000 grams • Kiloliter – 1000 liters • A meter divided by 1000 provides equal lengths of one millimeter McGraw-Hill

  8. Understanding Metric Notation (cont.) Common Metric System Prefixes McGraw-Hill

  9. Understanding Metric Notation (cont.) Combining Prefixes and Units McGraw-Hill

  10. Understanding Metric Notation (cont.) Rule 3-1 Use Arabic numerals, with decimals to represent any fractions. • Example: Write 1.25 g to represent 1 1/4 g Rule 3-2 If the quantity is less than 1, include a 0 before the decimal point. Delete any other zeros that are not necessary. • Example: Do not write .750; write 0.75 McGraw-Hill

  11. Understanding Metric Notation (cont.) Rule 3-3 Write the unit after the quantity with a space between them. • Example: Write 30 mg, not mg 30. Rule 3-4 Use lowercase letters for metric abbreviations. However, use uppercase L to represent liter. • Example: Write mg, not MG • Example: Write mL, not ml McGraw-Hill

  12. Answer Practice Considering Rules 3-1 to 3-4, which of these is the correct metric notation for six and two-eighths milliliters? a. 6.28mL b. ml 6.25 c. 6 mL d. 6.25 mL McGraw-Hill

  13. Converting within the Metric System Rule 3-5To 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. McGraw-Hill

  14. Practice 1. Convert 4 L to mL. 2. How many m are in 75 mm? ANSWER 4 L = 4.000 L = 4000 mL ANSWER 75 mm = 75.0 mm = 0.075 m McGraw-Hill

  15. Error Alert! • Remember: The larger the unit, the smaller the quantity. • The smaller the unit, the larger the quantity. 1 dollar bill = 4 quarters = 100 pennies 100 pennies = 4 quarters = 1 dollar bill Examples McGraw-Hill

  16. Apothecary System • Old system of measurement • First used by apothecaries (early pharmacists) • Household system evolved from it • Some older medications still are measured in apothecary units • Less familiar and apothecary units can be confused with metric units • Metric measurements are preferred in most cases McGraw-Hill

  17. Apothecary System • Units of measure • Dram ( ) – common unit of volume • Grain– basic unit of weight • Minim ( ) – common unit of volume • Ounce ( ) – fluid ounces of volume • Unit (USP Unit) – amount of medication to produce an effect McGraw-Hill

  18. Error Alert! • Do not confuse grains and grams • grains (gr) • grams (g) • 1 gr = 60 mg = 0.06 g • Do not confuse symbols for drams and ounces • = dram • = gram – has extra line on top • If unsure of order, ask physician who wrote it. McGraw-Hill

  19. Apothecary Notation Rule 3-6When 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. 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. McGraw-Hill

  20. ANSWER gr iv or gr iv Practice Using apothecary notation: 1. Write four grains 2. Write two and one-half grains 3. Write twelve ounces ANSWERgr iiss ANSWER xii McGraw-Hill

  21. Most familiar to patients Used with many OTC medications Least accurate Household notation places quantity before unit Units of measure Drop Teaspoon Tablespoon Ounce Cup Pint Quart Gallon Household System McGraw-Hill

  22. Apothecary and Household Equivalents • Units of measurement are equal • Apothecary ounces = household ounces • Neither based on multiples of 10 McGraw-Hill

  23. Abbreviations for Household Measures McGraw-Hill

  24. Apothecary and Household Equivalents (cont.) McGraw-Hill

  25. Practice Write the following in household notation: • Write six drops: • Write twelve ounces: ANSWER 6 gtt ANSWER 12 oz McGraw-Hill

  26. Practice How many teaspoons of solution are contained in 1 ounce of solution? ANSWER 1 oz = 2 x 1 tbs = 2 x 3 tsp = 6 tsp How many tablespoons are in ½ cup? ANSWER ½ cup = ½ x 1 cup = ½ x 8 oz = 4 oz = 4 x 1 oz = 4 x 2 tbs = 8 tbs McGraw-Hill

  27. 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. McGraw-Hill

  28. Milliequivalents and Units(cont.) • USP Units (U) • Insulin, heparin, and penicillin are measured in units (U). • Size of a unit varies for each drug. • International units (IU) – standardized by international agreement. • mEqs and U are not converted to other measures. McGraw-Hill

  29. Converting Among Systems • Must know how the measure of a quantity in one system compares to its measure in another system 1 tsp = 5 mL = 5 cc • Lose some exactness when converting among systems • gr 1 can equal 60 to 66.7 mg McGraw-Hill

  30. Equivalent Volume Measurements McGraw-Hill

  31. Equivalent Weight Measures McGraw-Hill

  32. Conversion Factors • Conversion factor – a fraction made of two equal quantities that are expressed in different units 1 kg = 2.2 lb provides two conversion factors: • 1 kg/2.2 lb • 2.2 lb/1 kg Example McGraw-Hill

  33. Conversion Factors (cont.) Rule 3-7When 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. McGraw-Hill

  34. Using Conversion Factors (cont.) Write a conversion factor for converting from milliliters to ounces. Example Write ounces as the numerator. The correct conversion factor is McGraw-Hill

  35. Using Conversion Factors:Fraction Proportion Method Procedure Checklist 3-1:Converting by the Fraction Proportion Method 1. Write a conversion factor with the units needed in the numerator and the units you are converting from in the denominator. 2. Write a fraction with the unknown, “?”, in the numerator and number to convert in the denominator. McGraw-Hill

  36. Using Conversion Factors:Fraction Proportion Method (cont.) Procedure Checklist 3-1:(cont.) 3. Set the two fractions up as a proportion. 4. Cancel units. 5. Cross-multiply, then solve for the unknown value. McGraw-Hill

  37. Using Fraction Proportion How many kg does a 62-pound child weigh? Example 62 x 1 = ? x 2.2 62 = 2.2 x ? 28.18 kg = ? McGraw-Hill

  38. 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 needed in the answer. 2. Write the second C:D so that C is the missing value and D is the number that isbeing converted. McGraw-Hill

  39. Using Conversion Factors:Ratio Proportion Method (cont.) Procedure Checklist 3-2:(cont.) 3. Write the proportion in the form A:B::C:D. 4. Cancel units. 5. Solve the proportion by multiplying means and extremes. McGraw-Hill

  40. Using Ration Proportion How many kg does a 66-pound child weigh? Example 1 kg = 2.2 lb First ratio is 1 kg:2.2 lb Second ratio is ?:66 lb 1 kg:2.2 lb::?:66 lb Solve for missing value ?=30 kg McGraw-Hill

  41. Using Conversion Factors:Dimensional Analysis Procedure Checklist 3-3:Converting by Dimensional Analysis 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. McGraw-Hill

  42. Using Conversion Factors:Dimensional Analysis Procedure Checklist 3-3: 3. Multiply the numerator of the conversion factor by the number that is being converted divided by 1. 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. McGraw-Hill

  43. Using Dimensional Analysis Convert 66 lb into kilograms. Example 1 kg = 2.2 lb ?/kg=1 kg/2.2 lb ? = 30 kg McGraw-Hill

  44. 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? ANSWER 10 mL:?::5 mL:1 tsp ? x 5 = 10 x 1 5 x ? = 10 ? = 2 tsp McGraw-Hill

  45. Practice Convert the following: 6 oz = ? mL ANSWER 180 mL Your patient is to receive 1.5 tbs of medicated mouthwash. How many cc of medicated mouthwash should the patient receive? ANSWER 22.5 mL McGraw-Hill

  46. Temperature • Both Fahrenheit (F) and Celsius (C) temperature scales are used in healthcare settings. • Celsius temperature is also known as Centigrade (C) temperature scale. • Water freezes at • 32 degrees Fahrenheit • 0 degrees Centigrade McGraw-Hill

  47. Temperature (cont.) • Water boils at • 212 degrees Fahrenheit • 100 degrees Celsius • Formulas used to convert between the systems McGraw-Hill

  48. Temperature (cont.) Rule 3-8Converting Between Temperature Systems 1. To convert from F to C use: 2. To convert from C to F use: (1.8 X °C) + 32 = °F McGraw-Hill

  49. Temperature (cont.) Rule 3-8 (cont.) 5F-160 = 9C can also be used to convert between Fahrenheit and Celsius. McGraw-Hill

  50. Practice Convert the temperatures. 35 °C = ? °F ANSWER 95 0F 103.6 °F = ? °C ANSWER 39.8 0C McGraw-Hill

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