54
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.
Key mathematical concepts
Whole numbers and fractions
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:
2
3
×
5
8
=
10
24
=
5
12
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,
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
