© 2010 The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill 3-1 Math and Dosage Calculations for Health Care Third Edition Booth & Whaley Chapter

© 2010 The McGraw-Hill Companies, Inc. All rights reservedMcGraw-Hill

3-1

Math and Dosage Calculations for Health Care Third Edition

Booth & Whaley

Chapter 3: Systems of Weights and Measures


3-2

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.

Learning Outcomes


3-3

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.

Learning Outcomes (cont.)


3-4

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


3-5

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

Dosage calculation


3-6

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

Basic Units of Metric Measurement


3-7

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


3-8

Understanding Metric Notation (cont.)

Prefix Length Valuekilo- (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 = = 0.001 m

micro- (mc) micrometer (mcm)

1 mcm = =

0.000001 m

m 100

1

m1000

1

m1,000,000

1

Common Metric System Prefixes


3-9


PrefixLength (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)

Combining Prefixes and Units


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Rule 3-1Rule 3-1 Use Arabic numerals, with decimals to represent any fractions. Example: Write 1.25 g to represent 1 1/4 g

Rule 3-2Rule 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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Rule 3-3Rule 3-3 Write the unit after the quantity with a space between them. Example: Write 30 mg, not mg 30.

Rule 3-4Rule 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



3-12

Practice

Considering Rules 3-1 to 3-4, which of these is the correct metric notation for six and two-eighths milliliters?

a. 6.28mLb. ml 6.25c. 6 mLd. 6.25 mL

41

Answer


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Rule 3-5Rule 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.

Converting within the Metric System


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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


3-15

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

ExamplesExamples


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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


3-17

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

Apothecary System


3-18

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.

Error Alert!


3-19

Rule 3-6Rule 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.

Apothecary Notation


3-20

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


3-21

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


3-22

Apothecary and Household Equivalents Units of

measurement are equal Apothecary

ounces = household ounces

Neither based on multiples of 10


3-23

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


3-24

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


3-25

Practice

Write the following in household notation: Write six drops:

Write twelve ounces:

ANSWER 6 gtt

ANSWER 12 oz


3-26

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


3-27

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.

10001


3-28

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.


3-29

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


3-30

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


3-31

Equivalent Weight Measures

Metric Apothecary

60 mg gr i (1 grain)

30 mg gr ss ( grain)

15 mg gr

1 mg gr

1 g (1000 mg) gr xv (15 grains)

0.5 g gr viiss (7 grains)

1 kg 2.2 lb

21

41

601

21


3-32

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

ExampleExample


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Rule 3-7Rule 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.

Conversion Factors (cont.)


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Write a conversion factor for converting from milliliters to ounces.

Write ounces as the numerator.

The correct conversion factor is

mL 30oz 1

Using Conversion Factors (cont.)

ExampleExample


3-35

Using Conversion Factors:Fraction Proportion Method

Procedure Checklist 3-1: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.


3-36

Procedure Checklist 3-1: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.

Using Conversion Factors:Fraction Proportion Method (cont.)


3-37

Using Fraction Proportion

How many kg does a 62-pound child weigh?

62 x 1 = ? x 2.262 = 2.2 x ?28.18 kg = ?

ExampleExample

kg 1lb 2.2

?lb 62


3-38

Using Conversion Factors:Ratio Proportion Method

Procedure Checklist 3-2: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.


3-39

Using Conversion Factors:Ratio Proportion Method (cont.)

Procedure Checklist 3-2: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.


3-40

Using Ration Proportion

How many kg does a 66-pound child weigh?

1 kg = 2.2 lbFirst ratio is 1 kg:2.2 lbSecond ratio is ?:66 lb1 kg:2.2 lb::?:66 lbSolve for missing value?=30 kg

ExampleExample


3-41

Using Conversion Factors:Dimensional Analysis

Procedure Checklist 3-3: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.


3-42

Using Conversion Factors:Dimensional Analysis

Procedure Checklist 3-3: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.


3-43

Using Dimensional Analysis

Convert 66 lb into kilograms.

1 kg = 2.2 lb

?/kg=1 kg/2.2 lb

? = 30 kg

ExampleExample

lb 2.21kg66lb kg ?


3-44

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?

ANSWER10 mL:?::5 mL:1 tsp? x 5 = 10 x 15 x ? = 10? = 2 tsp


3-45

Practice

Convert the following:

ANSWER 180 mL6 oz = ? mL

Your patient is to receive 1.5 tbsof medicated mouthwash. How many cc of medicated mouthwash should the patient receive?

ANSWER 22.5 mL


3-46

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


3-47

Temperature (cont.)

Water boils at 212 degrees Fahrenheit 100 degrees Celsius

Formulas used to convert between the systems


3-48

Temperature (cont.)

Rule 3-8Rule 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

C1.8

32 -F


3-49

Temperature (cont.)

Rule 3-8 Rule 3-8 (cont.)

5F-160 = 9C can also be used to convert between Fahrenheit and Celsius.


3-50

Practice

Convert the temperatures.

ANSWER 95 0F

ANSWER 39.8 0C

35 °C = ? °F

103.6 °F = ? °C


3-51

Time Traditional 12-hour clock

Source of errors in medication administration

Each time occurs twice daily 10:00 a.m. 10:00 p.m.


3-52

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


3-53

Time (cont.)

Rule 3-9Rule 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.


3-54

Time (cont.)

Rule 3-9Rule 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).


3-55

Practice

1. Convert 9:00 a.m. to international time.ANSWER 0900

2. Convert 12:19 a.m. to international time.ANSWER 0019

3. Convert 4:28 p.m. to international time.

ANSWER 1628


3-56

Practice

4. Convert 1139 to traditional time.ANSWER 1139 = 11:39 a.m.

5. Convert 1515 to traditional time.ANSWER 1515 = 3:15 p.m.


3-57

International Time

Rule 3-10Rule 3-10 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.


3-58

Practice

State the time 0900.*

State the time 1139.*

State the time 0023.* *Click speaker

buttons to hear

answers.


3-59

Apply Your Knowledge

Convert 5.0 mcg to mg.

ANSWER 5.0 mcg ÷ 1000 = 0.005 mg

Convert 43 kg to g.

ANSWER 43 x 1000 = 43,000 g


3-60


How many kg does an 88-pound child weigh?

ANSWER 88 lb = 2.2 lb

? 1 kg 88 x 1 = ? x 2.288 = 2.2 x ?40 kg = ?


3-61


Convert 50ºC to ºF.ANSWER

(1.8 x 50) + 32 = ºF(90) + 32 = ºF122 = ºF

Convert 100ºF to ºC.

C 37.78

C1.868

C1.8

32 100

ANSWER


3-62

End of Chapter 3

Practice is the best instruction of them all.

~Publilius Syrus

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© 2010 The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill 3-1 Math and Dosage Calculations for Health Care Third Edition Booth & Whaley Chapter