1. Pharmaceutical Calculations
Dr. Amani M. Elsayed

2. Objectives
Review basic mathematics
Review units of measure

3. Basic Mathematics Numerator Denominator Whole Numbers (10, 220, 5, 19)
Fractions
Parts of whole numbers (1/4, 2/7, 11/13)
Numerator
Denominator
Decimal Numbers
Another means of writing fractions
(1/2 =0.5, 1&3/4 = 1.75)

4. Basic Mathematics cont.
WARNING: Writing decimals incorrectly can lead to medication errors.
Trailing zeros
Write 5 not 5.0
Naked decimal points
Write 0.5 not .5
Periods are sometimes difficult to see leading to a 10 fold error.

5. Basic Mathematics cont.
Convert the following fractions to decimal numbers:
a. 1/2 b. 3/4 c. 1 d. 2/5
e. 1/3 f. 5/8 g. 50/100 h. 12/48
i. 11/2 j. 2 2/3 k. 5 1/4 l. 3 4/5

6. Units of Measure The Metric System
The most commonly used system in pharmacy.
Metric units prefixes are taken from International System of Units (SI units)
Adopted in 1960.

7. Units of Measure The Metric System
The metric system is based on the decimal system, in which everything is measured in multiples or fractions of 10.
Standard measures
Meter; Length
Gram; Weight
Liter; Volume
Prefixes
kilo-; 1000
milli-; 1/1000 = 0.001
micro-; 1/ =

8. Units of Measure The Metric System
Prefixes plus base units make up the metric system
Example:
Centi + meter = Centimeter
Milli + meter = ?
Micro + meter = ?

9. Units of Measure The Metric System
These prefixes are based on powers of 10.
What does this mean?
From each prefix every “step” is either:
10 times larger or
10 times smaller
For example
Centimeters are 10 times larger than millimeters
1 centimeter = 10 millimeters
kilo
hecto
deca
Base Units
meter
gram
liter
deci
centi
milli

10. Units of Measure cont. The Metric System
Volume is measured in cubic units (as milliliters or liters)
L = Liter
ml = milliliter
1 Liter = 1000 milliliters

11. Units of Measure cont. The Metric System
Mass measures the amount of matter in an object.
kg = kilograms
g = gram
mg = milligram
mcg = microgram or µg
ng = nanogram
1 kilogram = 1000 grams
1 gram = 1000 milligrams
1 milligram = 1000 micrograms
1 microgram = 1000 nanograms
Example
0.004kg = 4g = 4000mg = 4,000,000mcg

12. Problems # 1 Add 30 mg, 2.5 kg and 7.0 g. Express the answer in g.
Express the quantity of g as:
mg, kg, mcg
3) How many grams of aspirin would be needed to make 500 aspirin tablets if each tablet contains 325 mg of aspirin?

13. Answers 1)
30 mg = g
2.5 kg = g
7 g = g g
2) g = 1243 mg = kg = mcg
3) 500 x 325 = mg = g

14. Homework (1)
A capsule contains the following amounts of medicinal substances: g, 20 mg, g, 4 mg and 500 µg. What is the total weight of the substances in the capsule?
Multiply 820 ml by 12.5 and express the result in liters.
Divide g by 15 and express the result in milligrams.

15. Units of Measure cont. (Other Systems)
Avoirdupois – used in measuring bulk medications (pounds, ounces, grains)
Apothecary – developed after the Avoirdupois system to enable fine weighing of medications (pounds, ounces, drams, scruples, grains, gallons, pints, fluid ounces, fluid drams, minims)
Household – commonly used to measure liquids with home utensils (teaspoons, tablespoons, cups)

16. Units of Measure cont. (Equivalencies)
Equivalencies among systems
1 inch = 2.54 cm
1 kg = 2.2 pounds (lb)
1 fluid ounce (fl oz) = 29.57(30) milliliters (ml)
1 pint (pt) = (480) milliliters (ml)
1 teaspoonful (tsp) = 5 milliliters (ml)
1 tablespoonful (TBS) = 15 milliliters (ml)
1 ounce (oz) = grams (g)
1 pound (lb) = (454) grams (g)
1 ounce (oz) = grain (gr)

17. Problems # 2 Fill in the blanks: 1 liter (L) = ________ml
1000 g = __________kg
1 g = _____________mg
1000 mcg =_________mg
1 TBS = ____________tsp
1 TBS =_____________ml
2 fl oz =_____________ml
70 kg = ______________pounds (lb)

18. Answers Fill in the blanks: 1 liter (L) = 1000 ml 1000 g = 1 kg
1 g = 1000 mg
1000 mcg = 1 mg
1 TBS = 3 tsp
1 TBS = 15 ml
2 fl oz = 60 ml
70 kg = 154 pounds (lb)