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

Math for the Pharmacy Technician:
Concepts and Calculations
Egler • Booth

Chapter 3: Systems of

Measurement and Weight
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3-2

Systems of Weights and Measures

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3-3

Learning Objectives
When you have successfully completed Chapter 3, you will
have mastered skills to be able to:






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.

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3-4

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.

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3-5

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.

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3-6

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.”

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Table 3-1 Basic Units of Metric
Measurement

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3-8

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.



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3-9

Metric System

(con’t)



Length used for measurement such as
patient height.



Weight and volume are used to calculate
medications dosages.

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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.







3-10

Kilometer – 1000 meters
Kilogram – 1000 grams
Kiloliter – 1000 liters

When you divide a meter by 1000 equal
lengths, each length is one millimeter.

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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.



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3-12

Metric System Terms


Gram – measure unit of weight



Liter – unit of volume



Meter – unit of length



Centi- indicates

of the basic unit

1
100

 Kilo – prefix indicates basic unit times 1000
1
 Micro – indicates
of basic unit
1,000,000

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3-13

Basic Units of Metric
Measurement
Type of
Measure

Basic Unit

Abbreviation

Length

meter

m

Weight (or
Mass)

gram

g

Volume

liter

L

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Common Metric System

Prefixes

3-14

Prefix

Length

Value

kilo- (k)

kilometer
(km)

1 km = 1000 m

(basic unit)

meter (m)

1m

centi- (c)

centimeter
(cm)

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1 cm = 1 m
100
= 0.01 m

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3-15

Common Metric System
Prefixes (con’t)
Prefix

Length

Value

milli- (m)

millimeter
(mm)

1 mm = 1 m
1000
0.001 m

micro- (mc
or μ )

micrometer

(mcm)

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1 mcm =

1
m
= 1,000,000
= 0.000001

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3-16

Combining Prefixes and Units
(con’t)
Prefix

Length
(meter)

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

 
 
 

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Weight (Mass) Volume (liter)
(gram)

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Understanding Metric
Notation

3-17

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.

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Understanding Metric
Notation (con’t)

3-18

Write the unit after the quantity with a
space between them.


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For example: Write 30 mg, not mg 30.

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Understanding Metric
Notation (con’t)

3-19

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.

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3-20

Review and Practice


Determine the correct metric
notation for six and two-eighths
milliliters.

a.

b.
c.
d.

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6.28mL
ml1 6.25
4
6 mL
6.25 mL

Answer d. 6.25 mL

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Converting within the
Metric System

3-21

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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3-22

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
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3-23

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

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3-24

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.

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3-25

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

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