Pharmaceutical Calculations Dr. Amani M. Elsayed

Objectives Review basic mathematics Review units of measure

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)

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.

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

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.

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-; 1/1000000 = 0.000001

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

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

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

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

Problems # 1 Add 30 mg, 2.5 kg and 7.0 g. Express the answer in g. Express the quantity of 1.243 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?

Answers 1) 30 mg = 0.030 g 2.5 kg = 2500.000 g 7 g = 7.000 g 2507.030 g 2) 1.243 g = 1243 mg = 0.001243 kg = 1243000 mcg 3) 500 x 325 = 162500 mg = 162.5 g

Homework (1) A capsule contains the following amounts of medicinal substances: 0.075 g, 20 mg, 0.0005 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 0.465 g by 15 and express the result in milligrams.

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)

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) = 473.167 (480) milliliters (ml) 1 teaspoonful (tsp) = 5 milliliters (ml) 1 tablespoonful (TBS) = 15 milliliters (ml) 1 ounce (oz) = 28.35 grams (g) 1 pound (lb) = 453.59 (454) grams (g) 1 ounce (oz) = 437.5 grain (gr)

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)

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)