McKenna's Pharmacology, 2e

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C H A P T E R 5  Mathematics and dosage calculations

Multiplying two decimal numbers is a little more complex. Here it is important to add all of the decimal places from both numbers. For example: Multiplying 3.42 × 24.76, we can do a normal multiplication with the numbers as whole numbers 342 and 2476 which is 846792, then insert four decimal places which gives the final answer of 84.6792. Review the following examples: Dividing decimals Dividing decimals is less commonly used. However, similar to multiplying, dividing decimals by 10, 100, 1000 etc. also requires moving decimal points but to the left. For example: Dividing by 10, the decimal place is moved one decimal place, e.g. 3.45 ÷ 10 = 0.345 Dividing by 100, the decimal place is moved two decimal places, e.g. 534.2 ÷ 100 = 5.342 Dividing by 1000, the decimal place is moved three decimal places, e.g. 3298 ÷ 1000 = 3.298 MEASURING SYSTEMS The metric system is currently used in drug preparation and delivery in Australia and New Zealand and is the most widely used system of measure internationally. It is based on the decimal system, so all units are deter- mined as multiples of 10. This system makes the sharing of knowledge and research information easier. The metric system uses the gram as the basic unit of solid measure and the litre as the basic unit of liquid measure (see Table 5.1). Converting between different metric components is often required in calculating drug doses. Such conver- sions are similar to multiplying and dividing decimals. There are a number of key components to remember: 22.7 × 0.342 = 7.7634 0.87 × 0.54 = 0.4698 4.85 × 91.2 = 442.320 = 442.32

1000 micrograms (mcg) = 1 milligram (mg) 1000 mg = 1 gram (g) 1000 g = 1 kilogram (kg) 1000 millilitre (mL) = 1 litre (L)

Other systems Some drugs are measured in units. These measures may reflect chemical activity or biological equivalence. One of these measures is the unit. A unit usually reflects the biological activity of the drug in 1 mL of solution. The unit is unique for the drug it measures; a unit of heparin is not comparable to a unit of insulin. Milliequivalents (mEq) or millimoles (mmol) are used to measure electro­ lytes (e.g. potassium, sodium, calcium, fluoride). The milliequivalent refers to the ionic activity of the drug in question; the order is usually written for a number of milliequivalents instead of a volume of drug. Interna- tional units (IU) are sometimes used to measure certain vitamins or enzymes. These are also unique to each drug and cannot be converted to another measuring form. ■■ Safe and accurate drug administration requires sound mathematical skills. ■■ The metric system is the most widely used system of measure. ■■ Some drugs are measured in units. CALCULATING DOSE Drugs are made available only in certain forms or doses. Every time a nurse or midwife is required to administer any medication, the dose must be calculated to ensure the correct amount of drug is given. Oral drugs Frequently, tablets or capsules for oral administration are not available in the exact dose that has been ordered. In these situations, the person who is administering the drug must calculate the number of tablets or capsules to KEY POINTS KEY POINTS

■■ TABLE 5.1 Metric conversions System Solid measure

Liquid measure

litre (L) 1 millilitre (mL) = 0.001 L 1 mL = 1 cubic centimetre = 1 cc litre (L) 1000 mL = 1 L = 3.5 cups (c) 7 tablespoons (approx) = 100 mL 3 teaspoons (tsp) = 1 tbsp 60 drops (gtt) = 1 tsp

Metric

gram (g) 1 milligram (mg) = 0.001 g 1 microgram (mcg) = 0.000001 g 1 kilogram (kg) = 1000 g kilogram (kg) 1 kg = 1000 grams (g or gm)

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