Lecture Math for the pharmacy technician Concepts and calculations Chapter 3 – Lynn M. Egler, Kathryn A. Booth

Chapter 3, Systems of measurement and weight, reviews weights and measures. It introduces the metric system as well as apothecary and household systems. Time and temperature conversions are included. Special attention is given to conversion factors, and the procedures for ratio proportion, fraction proportion, and dimensional analysis methods are introduced as building blocks for later chapters.

Concepts and Calculations

Chapter 3: Systems of

Egler • Booth

Systems of Weights and Measures

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:

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.

 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.

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.”

Table 3-1 Basic Units of Metric

Measurement

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.

Metric System (con’t)

 Length used for measurement such

as patient height.

 Weight and volume are used to

calculate medications dosages.

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

 See Tables 3-2 and 3-3 in your

textbook to visualize these concepts.

 Kilo – prefix indicates basic unit times 1000

Metric System Terms

 Gram – measure unit of weight

 Liter – unit of volume

 Meter – unit of length

 Centi- indicates of the basic unit

100 1

1

Common Metric System

Common Metric System

micro- (mc

or μ )

micrometer (mcm)

1 mcm =

=

= 0.000001

m 1,000,000 1

m

1000 1

Combining Prefixes and Units

kilogram kg

kiloliter kL

milli-(1000)

millimeter mm

milligram mg

milliliter mL

Length (meter)

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.

Understanding Metric

Notation (con’t)

Write the unit after the quantity with

a space between them.

 For example: Write 30 mg, not mg 30.

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)

 Determine the correct metric notation

for six and two-eighths milliliters.

Answer d 6.25 mL

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.

Review and Practice

 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

Apothecary System

 An old system of measurement

 First used by apothecaries (early

pharmacists) and moved from Europe

 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

 The three common units of volume are

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.

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

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.

1 Write four grains using apothecary

3 Write twelve ounces using apothecary

notation.

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

Abbreviations for Household

Abbreviations for Household

Review and Practice

Write the quantity in Arabic numerals

before the abbreviation for the unit.

 Example: Write six drops using

Apothecary and Household

Equivalent Measures

tablespoon 1 tablespoon = 3 teaspoons

tablespoons

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

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.

1000 1

 USP Units (U)

 Medi cations such as insulin, heparin,

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

Table 3-8 Equivalent Weight

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

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.

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

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, “?”.

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.

Review and Practice

How many kg does a 62-pound

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

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.

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

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.

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

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

? = 30 kg

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

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?

 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

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.

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

Temperature (con’t)

Converting Between Temperature Systems

You can also use the formula

5F-160 = 9C

to convert between Fahrenheit and Celsius.

Review and Practice

Convert the temperatures.

Answer = 95 0 F

Answer = 39.8 0 C

35 0C = ? 0F

103.6 0F = ? 0C

 It can be a source of errors in

medication administration.

 Each time occurs twice daily.

 10:00 a.m.

 10:00 p.m.

Time (con’t)

 Military or international time

 Each time occurs only once per

day

 10:00 a.m = 1000

 10:00 p.m = 2200

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.

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).

Review and Practice

Convert 9:00 a.m to international

Review and Practice (con’t)

Convert 1139 to traditional time.

Convert 1515 to traditional time.

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.

Review and Practice

State the time 0900.*

Say “zero nine hundred.”

State the time 1139.*

Say “eleven thirty-nine.”

State the time 0023.*

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

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 ?

Review and Practice

122 = ºF

Convert 100ºF to ºC.

Systems of Weights and Measures

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.