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Expressing numbers and SI units
Learning outcomes
After reading the following chapter and undertaking personal study, you should be able to:
1 Identify situations in clinical practice in which numerical values are important.
2 Identify the following as two different ways in which numerical values are expressed:
(a) Scientific notation
(b) Numerical prefixes.
3 State what is mean by Système Internationale (SI) units.
4 Identify the units of measurement of the following:
(a) Length
(b) Mass
(c) Volume.
5 List situations in clinical practice in which the above units of measurement are used.
Introduction
Most students who chose nursing as a career do so because they are interested in people. They do not necessarily get enthusiastic about mathematics! Nonetheless, being interested in people and being concerned to use numbers correctly certainly do go together. For example, think about the issue of unplanned teenage pregnancy in the UK. Why is it important? Apart from concern for individuals involved, teenage pregnancy in the UK is important because the numbers involved are high compared with those in other European countries. We might now start to think about why this is so, but it is numbers that have triggered our concern. Similarly, we might try to develop a programme to deal with teenage pregnancy, but how would we know whether it was successful? Once again, we come back to numbers. Even the most human, people-centred issues with significant ethical aspects involve numbers at some point. Numbers are also involved in a number of the important day-to-day tasks that nurses undertake. For example, nurses dispense drugs in specific doses, and some nurses prescribe drugs. We adjust the rate at which fluid is flowing in an intravenous infusion (drip) or the energy of the electric shock delivered by a defibrillator used to restart a heart that has stopped beating. In each of these cases, it is of the utmost importance that we get the numbers right. Clearly we do not want to endanger a patient by giving too much of a drug, by overloading the circulation with fluid or by administering a shock of too great an energy. At times, we have to deal with very small numbers such as the dose of some drugs, while at other times the numbers are quite large – energy values of food, for example.
Expressing numbers
When, as nurses, we have a problem with numbers, to whom do we look for help? Perhaps we should turn to people whose main business is numbers. Scientists understand the problems that numbers present, since they have to deal with a very wide range of numerical values. Consider the following two extremes: the earth, which is very large, and the hydrogen atom, which is very small. The mass of each is as follows:
The earth = 5 980 000 000 000 000 000 000 000 kg.
The hydrogen atom = 0.000 000 000 000 000 000 000 000 001 674 kg.
1The range of values that health-care professionals meet is not quite so wide, but sometimes we do find ourselves writing out a great many zeros. We could write very large or very small numbers in a more convenient way by doing what scientists do – using scientific notation.
Scientific notation
Have you ever wondered why we write numbers as we do? In human history, numbers have been written in different ways. For example, the Romans expressed numbers as letters, e.g. I, II, III, IV, V. Fortunately for them, they did not have to deal with something as big as the earth or as small as an atom. Still today, we sometimes use simple tally systems for counting – for example, making a mark each time a count is made, e.g. l, ll, lll, llll. At the count of five, we usually score through a group of four and start again, thus IIII; we can then readily add up groups of five. The point is to note that there is more than one way to write numbers, and scientific notation is simply one way to make very large or small numbers easier to record. To change a large number to scientific notation, move the decimal point to the left and place it between the first and second digits. Next, count the number of spaces moved and write this figure as a power of 10.
What does power of 10 mean? It is simply a way of showing how many times you moved the decimal point. For example:
100 = 10 × 10 or as a power of ten = 1 × 10
2 (or simply 10
2)
1000 = 10 × 10 × 10 or as a power of ten = 1 × 10
3 (or simply 10
3)
Using scientific notation, the mass of the earth becomes 5.98 × 1024 kg.
What about very small numbers? To change a small number to scientific notation, move the decimal point to the right and stop immediately after the first digit that is not a zero. To show that you have moved the decimal point to the right, express the power of 10 as a negative value. In this way, the mass of a hydrogen atom becomes 1.674 × 10-27 kg.
Is there not an even more convenient method of expressing very large and very small numbers? Indeed there is – we could use numerical prefixes.
Numerical prefixes
A prefix is a word that is added before another in order to change its size. Let us take an everyday example. A ‘store’ is a shop – right? So what, then, is a ‘megastore’? Yes – it is a big shop. We can tell it is a big shop from the prefix ‘mega’, which means big. Actually, ‘mega’ is a numerical prefix with a precise meaning – it means one million. So, then, numerical prefixes are used to replace powers of 10. We use numerical prefixes all the time; for example, we do not usually say ‘two thousand metres’ but ‘two kilometres’. ‘Kilo’ is a numerical prefix that means one thousand. We also use prefixes to deal with very small numbers (sub-powers of ten). Let us use an example from our bodies. Instead of writing the diameter of an erythrocyte (red blood cell) as 0.000 008 m (or 8 × 10-6 m), we could use the numerical prefix ‘micro’, which means one-millionth. Now we say that the erythrocyt...
