Proportions are routinely used in dosage calculations. For example, how many milligrams of the drug ibuprofen are present in 10 milliliters (10 mL) when there are 20mg of ibuprofen in each mL. A proportion can be set as: 1(mL) 20(mg) _____ = ______ 10 (mL) x(mg) 10 * 20 x = ________ = 200mg

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4 Use of proportions is very common in dosage calculations, especially in finding out the drug concentration per teaspoonful or in the preparation of bulk or stock solutions of certain medications. In a given proportion, when any three terms are known, the missing term can be determined. For example, if a/b = c/d, then a = bc/d, or any other term can be calculated from the other three known terms. For example, to find out how many milligrams of a drug is present in 5 mL when there are 20 mg of that drug in 1 mL, a proportion can be set as: Drug: volume = drug: volume 20mg:1 mL = X mg:5 mL X = 20 * 5 = 100 mg Percentage The word percent mean “hundredths of a whole” and is express with a % symbol. Consequently 1% is the same as the fraction 1/100 or the decimal 0.01. To convert a fraction to a percent, divide the numerator of the fraction by the denominator, multiply by 100 (move the decimal point two places to the right), round the answer to the desired precision if necessary, and place the % symbol next to the numeric value. Example: Convert 3/5 to a percent 3 ÷ 5 = 0.60 0.60 X 100 = 60% To convert a percent to a fraction, remove the percent symbol, make a fraction with the percent as the numerator and 100 as the denominator, and reduce the fraction to its lowest possible terms. Example: Convert 60% to a fraction 60/100 = 3/5

5 To convert a decimal to a percent, multiply the decimal by 100 and add a percent symbol to the number. Example: Convert 0.75 to a percent 0.75 * 100 = 75% To convert a percent to a decimal, drop the percent symbol and then divide the numerator by 100. Example: 45% = 45/100 = 0.45 Another useful tool is being able to determine percentage. How much is X as a percent of Y? The formula is as follows: (X÷Y) * 100 = Z% Example: How much is 56 of 82? 56 ÷ 82 = 0.6829 0.6829 * 100 = 68.29% (rounded)

6 Fractions and Decimal Equivalents As a technician, you work in a very fast paced environment. It would be very helpful to have certain fraction and decimal equivalents memorized so that you can quickly make these conversions when necessary. Some common equivalent decimals and fractions are listed below: 0.1and 1/10 0.2and 1/5 0.25 and ¼ 0.50 and ½ 0.75 and ¾ 1.0 and 1/1 or 2.2 or 1 To convert a fraction to a decimal, divide the numerator by the denominator, and round the answer to the desired precision if necessary. Example: Convert 3/9 to a decimal 3 ÷ 9 = 0.3333

7 Section II Applying Systems of Measurements Many calculations have been simplified by the shift from apothecary to metric system of measurements. Unfortunately, there are still a significant amount of calculation errors. Most of these errors occur because of simple mistakes in arithmetic. Metric System The metric system appears in the official listing of drugs in the United States Pharmacopoeia (USP). The metric system of measurement was first developed by the French and is the most commonly used system for prescribing and administering medications. The basic units, multiplied or divided by 10, make up the metric system (the units are based on multiples of 10). The knowledge of decimals, reviewed in Section 1 will be useful in this section.