C H A P T E R 5
Mathematics and dosage calculations
55
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:
22.7
×
0.342 = 7.7634
0.87
×
0.54 = 0.4698
4.85
×
91.2 = 442.320 = 442.32
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:
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.
KEY POINTS
■■
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
■■
TABLE 5.1 Metric conversions
System
Solid measure
Liquid measure
Metric
gram (g)
1 milligram (mg) = 0.001 g
1 microgram (mcg) = 0.000001 g
1 kilogram (kg) = 1000 g
litre (L)
1 millilitre (mL) = 0.001 L
1 mL = 1 cubic centimetre = 1 cc
Household
kilogram (kg)
1 kg = 1000 grams (g or gm)
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
