McKenna's Pharmacology, 2e

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P A R T 1  Introduction to nursing pharmacology

BASIC MATHEMATICAL CALCULATIONS Accurate and safe medication administration relies upon accurate mathematic skills, including addition, subtrac- tion, multiplication and division. In this area, an error can be potentially fatal. Nurses and midwives, there- fore, have a responsibility to calculate medication doses exactly, and this relies on sound mathematical skills. Calculators are commonly used in clinical practice to aid calculations of drug dosages. Calculation errors with calculators can result in large miscalculations. Nurses and midwives choosing to use calculators also need to undertake mental calculations in conjunction with using the calculator to avoid potentially disastrous outcomes. A whole number is a number that is complete. On the other hand, a fraction is a part of a number. For example, 1 / 2 is a fraction that is part of the whole number 1. Fractions contain a numerator (top number) and denominator (bottom number), for example, in 1 / 2 , the numerator is 1, and the denominator is 2. Proper fractions are those where the numerator is less than the denominator, while improper fractions are the reverse where the numerator is larger than the denominator. For example: 1 / 4 is a proper fraction while 6 / 4 is an improper fraction. Finally, a mixed number is one that contains both a whole number and a fraction, for example, 5 1 / 4 . Mixed numbers can be converted into improper fractions. For example, 5 1 / 4 can also be expressed as 21 / 4 . When calculating drug doses, it is common to have to simplify fractions into smaller numbers. In order to do this, both the numerator and the denominator need to be divided by the same (common) number. For example: if simplifying 20 / 100 , it can be seen that 20 can be divided into both numbers. By doing this, the fraction can be sim- plified to 1 / 5 and cannot be further simplified. Multiplying fractions Sometimes it is necessary to multiply two different frac- tions. To do this, multiply both numerators and both denominators, then simplify use the common factor. For example: Decimals and decimal places Decimals are numbers that contain decimal points and are a different way to present fractions. These points rep- resent parts of the number 10, such as 6.125 or 23.44. They are most commonly used in liquid drug prepara- tion. We refer to decimal places as the number of places after the decimal point. For example, 2 3 × 5 8 = 10 24 = 5 12 Key mathematical concepts Whole numbers and fractions

65.4 has one decimal place 1.23 has two decimal places 2.387 has three decimal places

Converting decimals to fractions It is important to be able to convert between decimal numbers and fractions. For example, 7.5 can be expressed as 7 5 / 10 . Simplifying this further by dividing the fraction by the common factor of 5, we can express this as 7 1 / 2 . Examples: 5.4 = 5 4 / 10 = 5 2 / 5 1.25 = 1 25 / 100 = 1 1 / 4 53.6 = 53 6 / 10 = 53 3 / 5 Converting fractions to decimals Sometimes we also need to convert the other way, that is, fractions to decimals. For example, using the fraction 5 1 / 4 , expressing this as a decimal would be 5.25. In order to convert the fraction to a number out of 10, it is neces- sary to divide the numerator by the denominator. Examples: 23 2 / 3 = 23.67 10 1 / 2 = 10.5 56 7 / 8 = 56.875 Rounding decimal numbers Sometimes it is necessary to round decimal numbers containing many decimal places to one or two. The general principle in rounding decimals is that if the number in the last decimal place is 5 or more, we round the next decimal place up by one. If it is 4 or less, we round this number down. For example, rounding 5.436 to two decimal places becomes 5.44. Rounding 6.33 to one decimal place becomes 6.3, while rounding 2.35

to one decimal place becomes 2.4. Examples: One decimal place

2.54 = 2.5 3.98 = 4.0 Two decimal places 2.453 = 2.45 0.656 = 0.66 Three decimal places 0.2134 = 0.213 8.7935 = 8.794

Multiplying decimals Sometimes it is necessary to multiply two decimal numbers. Multiplying decimals by 10, 100, 1000 etc. is easy and requires moving decimal points to the right. For example: Multiplying by 10, the decimal place is moved one decimal place, e.g. 3.45 × 10 = 34.5 Multiplying by 100, the decimal place is moved two decimal places, e.g. 4.931 × 100 = 493.1 Multiplying by 1000, the decimal place is moved three decimal places, e.g. 5.124 × 1000 = 5124