UsinG Pharmaceutical Calculation

Techniques and Terminologies

HLT PHS3 M04 02 22
LO1. Use dimensional analysis to convert
one unit to another
Elias.s (B.Pharm)
21/01/2025 1
Objectives

At the end of this module the trainers are able to:-

 Identify and used the dimensional analysis methods to
convert
one unit to another
 Described pharmaceutical terminologies and medical
terminology
during preparations of dosage forms

 Identify and use pharmaceuticals preparations materials

Introduction

• Pharmacy is the art and science of preparing and dispensing

medication and the provision of drug related information to the public

and health care providers

• Scope of pharmacy
 By what area the pharmacy studied or applied
 Industrial pharmacy
 Quality control, regulatory area, research and laboratory,
whole sale and distributor, retail outlet, academic, consultant,
nuclear pharmacy, clinical pharmacy and hospital.
Pharmaceutics
Pharmakon: - drug
Ceutics: - Technique, Dosage design or formulation of drugs.

Pharmaceutics: - is the science of dosage form design or

preparation.

 It deals about drug dosage design or drug formulation

 Study on the: formulation, manufacture, stability, and

effectiveness of pharmaceutical dosage forms.

Definition :-
 Pharmaceutical calculation is the area of study that applies the basic

principle of mathematics to the preparation, safe and effective use of

pharmaceuticals.

 Perfecting basic mathematical functions will help to attain the goal of

100 percent accuracy desired in pharmacy.

 1.1 Numbers and numerals
Number?
Total quantity or amount
Abstract/pure  without any unit of measurement
Concrete/denominate with unit
Numeral?
a word,
sign, or
group of words and signs representing a number

7
 cont.…

Numeral
 Arabic numerals,
o 0-9
 Roman numerals
o I, II, III,IV,V…
 Ethiopian/Geez numerals
o , , , ,…, , …, 

8
 Cont….

Arabic Numerals
Used universally to indicate quantities
Represented by a zero and nine digits
Easy to read and less likely to be confused

9
 Cont…
Ethiopian/Geez Numerals
Not commonly used
Mostly used in churches

1 2 3 4 5 6 7 8 9 10

፩ ፪ ፫ ፬ ፭ ፮ ፯ ፰ ፱ ፲

20 30 40 50 60 70 80 90 100

፳ ፴ ፵ ፶ ፷ ፸ ፹ ፺ ፻

1000 10,000 100,000 1,000,000 100,000,000 1,000,000,000

፲፻ ፻፻ ፲፻፻ ፻፻፻ ፻፻፻፻ ፲፻፻፻፻

10
 cont…

Roman Numerals
Used with the apothecary’s system of measurement to designate
quantities on prescription
The Roman system of notation expresses a fairly large range of
numbers by the use of a few letters of the alphabet in a simple
"positional" notation indicating adding to or subtracting from a
succession of bases.

11
 cont…
Roman Numerals and Their Arabic Equivalents

12
 cont…
Rules
In the usage of Roman numerals, the following set of rules apply:
(1) When a Roman numeral is repeated, it doubles its value; when a
Roman numeral is repeated three times, it triples its value.
Example
I = 1,
II = 2,
III = 3,
X = 10,
XX = 20,
XXX = 30
13
 cont…

(2) When Roman numeral(s) of lesser value follows one of a greater

value, they are added.
Examples:
VII = 5 + 1 + 1 = 7
XVI = 10 + 5 + 1 = 16
(3) When Roman numeral(s) of lesser value precedes one of a greater
value, they are subtracted from the greater value numeral Examples:
IV = 5 − 1 = 4
IX = 10 − 1 = 9

14
 Cont…
(4) When Roman numeral of a lesser value is placed between two
greater values, it is first subtracted from the greater numeral placed
after it, and then that value is added to the other numeral(s)
Examples:
XXIX = 10 + 10 + (10 − 1) = 29
XIV = 10 + (5 − 1) = 14
(5) Roman numerals may not be repeated more than three times in
succession.
Example: 4 is written as IV but not as IIII

15
 cont…

6) When possible, largest value numerals should be used. Example: 15

is written as XV but not as VVV
Roman numerals are sometimes combined with the abbreviation
for one half, ss.
Roman numerals are written in lowercase when used with ss, such
as iss to indicate 1 ½ .

16
 cont.…
Examples
1. Convert in to Arabic numerals
A. Roman
a. LXXVII 1. A:
b. MDCCLXXVI a. 77
c. CDXC
b. 1776
B. Ethiopian
c. 490
B:
a. 
d. 78
b. 
e. 150
c.  f. 490
2. Convert in to roman numerals 2. -
3999 MMMCMXCIX
17
Main components or branches of
pharmaceutics
1. Physical pharmacy:- concerned with basic
physical chemistry necessary for the efficient design
of dosage forms.
 It aids the pharmacist predict the solubility,
compatibility and biologic action of the drug product.
2. Industrial pharmacy: - concerned with dosage
form design, product processing, packaging,
evaluation and regulation etc
3. Pharmacokinetics: - involves the kinetics of drug
absorption, distribution, metabolism and excretion.
5.Pharmaceutical microbiology and
immunology:- concerned with the cultivation and
elimination of microorganisms in medicines.

6. Pharmacy practice( social pharmacy ) is

according to National Association of Boards of
Pharmacy(NABP) the practice of pharmacy involves the:-
 Interpretation
 Evaluation and implementation of prescription drugs
 Dispensing of prescription drugs
 Participation in the selection of drugs n medical device
 Administration of medication
Dimensional Analysis
• dimensional analysis (also known as factor analysis, factor-label
method, or unit-factor method).
• It is a process that you use to change from one unit to another using
conversion factor.
• Some terms are inverted (to their reciprocals)
to permit the cancellation of like units in the numerator(s) and
denominator(s)
and leave only the desired terms of the answer.

• One advantage of using dimensional analysis is the consolidation of

several arithmetic steps into a single equation.
reduces errors and can be used for all dosage calculations
Dimensional Analysis:
• Four major steps that should be performed for
successful dimensional analysis;
1- Find the Final unite
2- Identify the given unite
3- Apply any conversion factors
4- Set up ratios so that cancelations lead to
the final unite.
Equalities

State the same measurement in two different units

length

10.0 in.

25.4 cm
 Conversion Factors

Fractions in which the numerator and denominator are EQUAL

quantities expressed in different units

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm

2.54 cm 1 in.
How many minutes are in 2.5 hours?

Conversion factor

2.5 hr x 60 min = 150 min

1 hr

cancel
By using dimensional analysis / factor-label method, the UNITS
ensure that you have the conversion right side up, and the UNITS
are calculated as well as the numbers!
• Example: IV Dose
Administer digoxin 0.5 mg IV daily. The drug
concentration available from the pharmacy is digoxin
0.25 mg/mL. How many mL will you need to administer a
0.5 mg dose?

Step 1: What unit of measure (label) is needed? Place this

on the left side of the equation
Step 2: On mL?=
the right side, place the information given with the same
label needed in the numerator. In this example, we know that the drug
concentration available is 0.25 mg/mL. Place mL in the numerator and
0.25 mg in the denominator.
Step 3: The desired dose is 0.5 mg. Place information with the same
label as the preceding denominator into the equation in the
numerator to cancel out the unwanted labels. Repeat this step
sequentially until all unwanted labels are canceled out.

Step 4. Multiply numbers across the numerator, then multiply all the
numbers across the denominator. Divide the numerator by the
denominator for the final answer with the correct label.
 Metric System
• There are two systems of weights and measures
1.The imperial system is old system of weights and measures
 divided into two parts
• Avoirdupois system
• Pound (Lb), Standard unit
• Apothecaries system
• The grain is the standard weight

2. Metric System
A metric system is a system of measurement based on the
standard units as a meter for length, kilogram for mass, and
liter for volume.
• This familiar system with its base units are (meter, litter, and
kilogram)
• It is fundamental to the practice of pharmacy.
• Cont…

universally accepted as the International System of Units

called the SI System. Many countries follow this system.
• The Metric system has 3 main units namely,
meter to measure the length,
 kilogram to measure the mass, and
seconds to measure time.
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.

3-29
Metric System (con’t)

• Length used for measurement such as patient height.

• Weight and volume are used to calculate medications dosages.

3-30
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.
• Kilometer – 1000 meters
• Kilogram – 1000 grams
• Kiloliter – 1000 liters
• When you divide a meter by 1000 equal lengths, each length is one
millimeter.

3-31
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.

3-32
Metric System Terms
• Gram – measure unit of weight
• Liter – unit of volume
• Meter – unit of length
1
• Centi- indicates of the basic unit
100

 Kilo – prefix indicates basic unit times 1000

1
 Micro – indicates of basic unit
1,000,000

3-33
Basic Units of Metric
Measurement

Type of Basic Unit Abbreviation

Measure
Length meter m

Weight (or gram g

Mass)
Volume liter L

3-34
Common Metric System
Prefixes
Prefix Length Value
kilo- (k) kilometer 1 km = 1000 m
(km)

(basic unit) meter (m) 1m

centi- (c) centimeter 1 cm = 1 m

100
(cm) = 0.01 m

3-35
Common Metric System
Prefixes (con’t)

Prefix Length Value

milli- (m) millimeter 1 mm = 1 m

1000
(mm) 0.001 m

micro- (mc micrometer 1 mcm =

or μ ) (mcm)
1
= 1,000,000m
= 0.000001

3-36
Combining Prefixes and Units
(con’t)

Prefix Length Weight (Mass) Volume (liter)

(meter) (gram)

kilo-(x1000) kilometer kilogram kiloliter

km kg kL

centi-(100) centimeter centigram centiliter

cm cg cL
milli-(1000) millimeter milligram milliliter
mm mg mL

micro- micrometer microgram mcg microliter

( 1,000,000) mcm mcL
3-37
Understanding Metric
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.

3-38
Understanding Metric
Notation (con’t)

Write the unit after the quantity with a space

between them.

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

3-39
Understanding Metric
Notation (con’t)
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.

3-40
 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.

3-41
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

3-42
 Measure of Length
Length is measured in meters. The unit is denoted by the
alphabet (m).
• 1 meter = 0.001 kilometre
= 0.01 hectometre
= 0.1 dekametre
= 10 decimetres
= 100 centimetres
= 1000 millimetres
= 1,000,000 micrometres
=1,000,000,000 nanometres
• Equivalencies of the most common length
denominations:

• 1000 millimetres (mm)= 100 centimetres

(cm)
100 centimetres (cm) = 1 meter (m)
• As a point of reference, 1 inch is equivalent to
2.54 centimetres or 25.4 millimetres, 1 foot =
12 inches
 Measure of Volume

The liter is the primary unit of volume. It represents the volume

of the cube of one tenth of a meter, that is, of 1 dm3.
The United States Pharmacopeia—National Formulary2states: ‘‘One
millilitre (mL) is used herein as the equivalent of 1 cubic centimetre (cc).’’
The table of metric volume: • This table may also be written:
1 kilolitre (kL) = 1000.000
litters
1 liter =0.001 kilolitre
1 hectolitre (hL) = 100.000 = 0.010 hectolitre
liters = 0.100 dekalitre
1 dekalitre (daL) = 10.000 liters = 10 decilitres
1 liter (L) = 1.000 liter = 100 centilitres
1 decilitre (dL) = 0.100 liter = 1000 millilitres
1 centilitre (cL) = 0.010 liter
1 millilitre (mL) = 0.001 liter = 1,000,000
1 microliter (L) = 0.000,001 microliters
liter • 1cc/1cm3 =1ml
 Measure of Weight
The primary unit of weight in the SI is the gram, which is the
weight of 1 cm3 of water at 40C ,its temperature of greatest
density.
 measuring the weight of the amount of medication in a
solid dosage form
 indicating the amount of solid medication in a solution
 expressing the weight of a patient or in a counterbalance
measuring weight

Pharmaceutical dosages are commonly expressed in grams (g)

or milligrams (mg).
For example, you may fill a prescription for 1 g tablet per day of
the anti-ulcer medication sucralfate.
or prepare a 600 mg antibiotic suspension of
The table of metric
weight: • This table may also be written:
• 1 gram = 0.001 kilogram
1 kilogram (kg) = 1000.000 = 0.010 hectogram
grams = 0.100 dekagram
1 hectogram (hg) = 100.000 = 10 decigrams
grams = 100 centigrams
1 dekagram (dag) = 10.000 = 1000 milligrams
grams = 1,000,000
1 gram (g) = 1.000 micrograms
gram = 1,000,000,000
1 decigram (dg) = 0.1000 nanograms
gram =1,000,000,000,000
1 centigram (cg) = 0.010 gram picograms
1 milligram (mg) = 0.001 =1,000,000,000,000,000
gram femtograms
1 microgram (g or mcg) =
• Equivalencies of the most common
weight denominations:
1000 micrograms ( mcg) =1
milligram (mg)
1000 milligrams (mg) =1
gram (g)
1000 grams (g) =1
kilogram (kg)
 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
 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
5 x ? = 10
?=2
3-50
• A medication order calls for 1000 milliliters of a dextrose
intravenous infusion to be administered over an 8-hour period.
Using an intravenous administration set that delivers 10
drops/milliliter, how many drops per minute should be delivered
to the patient?
Solving by dimensional analysis:
8 hours = 480 minutes (min.)
THANKS