1. Chapter 3: Systems of Weights and Measures
Math and Dosage Calculations for Health Care Third Edition Booth & Whaley
Chapter 3: Systems of Weights and Measures
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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.
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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.
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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
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5. Metric System Most widely uses system of measurement Basic units
Named for the meter (basic unit of length).
A meter = inches
Basic units
Meter – length for measurements of height, circumference, wound size
Gram – weight
Liter - volume
Dosage calculation
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6. Metric System (cont.)
Basic Units of Metric Measurement
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
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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
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8. Understanding Metric Notation (cont.)
Common Metric System Prefixes
Prefix
Length
Value
kilo- (k)
kilometer (km)
1 km = 1000 m
(basic unit)
meter (m)
1 m
centi- (c)
centimeter (cm)
1 cm = = 0.01 m
milli- (m)
millimeter (mm)
1 mm = = m
micro- (mc)
micrometer (mcm)
1 mcm = = m
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9. Understanding Metric Notation (cont.)
Combining Prefixes and Units
Prefix
Length (meter)
Weight / Mass (gram)
Volume (liter)
kilo- (x 1000)
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)
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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
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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
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12. Practice
Considering Rules 3-1 to 3-4, which of these is the correct metric notation for six and two-eighths milliliters?
a mL
b. ml 6.25
c mL
d mL
Answer
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13. Converting within the Metric System
Rule 3-5 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.
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14. Practice 1. Convert 4 L to mL. 2. How many m are in 75 mm?
ANSWER 4 L = L = 4000 mL
ANSWER 75 mm = 75.0 mm = m
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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
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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
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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
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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.
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19. Apothecary Notation
Rule 3-6 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.
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.
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20. Practice Using apothecary notation: 1. Write four grains
2. Write two and one-half grains
3. Write twelve ounces
ANSWER gr iv or gr iv
ANSWER gr iiss
ANSWER xii
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21. Household System 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
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22. Apothecary and Household Equivalents
Units of measurement are equal
Apothecary ounces = household ounces
Neither based on multiples of 10
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23. Abbreviations for Household Measures
Unit
Abbreviation
Drop
gtt
Teaspoon
tsp, t
Tablespoon
tbsp, T
Ounce
oz or
Unit
Abbreviation
Cup
cup or c
Pint pt
Quart qt
Gallon
gal
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24. Apothecary and Household Equivalents (cont.)
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
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25. Practice Write the following in household notation: Write six drops:
Write twelve ounces:
ANSWER 6 gtt
ANSWER 12 oz
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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
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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.
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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.
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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
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30. Equivalent Volume Measurements
Metric
Household
Apothecary
5 mL
1 tsp
1 dr
15 mL
1 tbsp
3 or 4 dr
30 mL
2 tbsp = 1 oz
1 oz = 8 dr
240 mL
8 oz = 1 c
8 oz
480 mL
2 c = 1 pt
16 oz
960 mL
2 pt = 1 qt
32 oz
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31. Equivalent Weight Measures
Metric
Apothecary
60 mg
gr i (1 grain)
30 mg
gr ss ( grain)
15 mg gr
1 mg
1 g (1000 mg)
gr xv (15 grains)
0.5 g
gr viiss (7 grains)
1 kg
2.2 lb
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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
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33. Conversion Factors (cont.)
Rule 3-7 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.
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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
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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.
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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.
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37. Using Fraction Proportion
How many kg does a pound child weigh?
Example
62 x 1 = ? x 2.2
62 = 2.2 x ?
28.18 kg = ?
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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 is being converted.
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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.
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40. Using Ration Proportion
Example
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 lb
1 kg:2.2 lb::?:66 lb
Solve for missing value
?=30 kg
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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.
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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.
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43. Using Dimensional Analysis
Convert 66 lb into kilograms.
Example
1 kg = 2.2 lb
?/kg=1 kg/2.2 lb
? = 30 kg
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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
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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 mL
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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
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47. Temperature (cont.) Water boils at
212 degrees Fahrenheit
100 degrees Celsius
Formulas used to convert between the systems
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48. Temperature (cont.) Rule 3-8 Converting 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
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49. Temperature (cont.) Rule 3-8 (cont.)
5F-160 = 9C can also be used to convert between Fahrenheit and Celsius.
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50. Practice Convert the temperatures. 35 °C = ? °F 103.6 °F = ? °C
ANSWER F
103.6 °F = ? °C
ANSWER C
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51. Time Traditional 12-hour clock
Source of errors in medication administration
Each time occurs twice daily
10:00 a.m.
10:00 p.m.
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52. Time (cont.) 24-hour clock Military or international time
Reduces chance for errors
Each time occurs only once per day
10:00 a.m. = 1000
10:00 p.m. = 2200
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53. Time (cont.)
Rule 3-9 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.
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54. Time (cont.) Rule 3-9 (cont.)
4. 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.
5. Write midnight as either 2400 (international) or 0000 (military time).
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55. Practice 1. Convert 9:00 a.m. to international time. ANSWER 0900
3. Convert 4:28 p.m. to international time.
ANSWER
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56. Practice 4. Convert 1139 to traditional time.
ANSWER = 11:39 a.m.
5. Convert 1515 to traditional time.
ANSWER = 3:15 p.m.
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57. International Time
Rule 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.
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58. *Click speaker buttons to hear answers.
Practice
State the time 0900.*
State the time 1139.*
State the time 0023.*
*Click speaker buttons to hear answers.
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59. Apply Your Knowledge Convert 5.0 mcg to mg. Convert 43 kg to g.
ANSWER mcg ÷ 1000 = mg
Convert 43 kg to g.
ANSWER x 1000 = 43,000 g
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60. Apply Your Knowledge How many kg does an 88-pound child weigh? ANSWER
88 lb = 2.2 lb
? 1 kg
88 x 1 = ? x 2.2
88 = 2.2 x ?
40 kg = ?
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61. Apply Your Knowledge Convert 50ºC to ºF. Convert 100ºF to ºC. ANSWER
(1.8 x 50) + 32 = ºF
(90) + 32 = ºF
122 = ºF
Convert 100ºF to ºC.
ANSWER
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62. End of Chapter 3 Practice is the best instruction of them all.
~Publilius Syrus
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