as a decimal.
30 How many millilitres are there in 0.006 litres?
Feedback and suggested actions
If you made a mistake or had any difficulty with questions 1 or 8, you’ll find more guidance about this in Chapter 2 in the ‘Addition’ section.
If questions 4, 11 or 23 gave you problems, the ‘Subtraction’ section in Chapter 2 should help you.
If questions 6, 10, 13 or 16 caused you any difficulties, the section in Chapter 2 on ‘Multiplication’ should provide you with the techniques and practice questions to overcome these.
If question 18 caused problems, go to the ‘Division’ section of Chapter 2.
If you had problems with questions 2, 5, 9, 12 or 17, go to ‘The decimal system’ section in Chapter 2.
If questions 3, 7 or 14 tripped you up, start your reading at the beginning of Chapter 2 where you’ll find more information.
Questions 15, 20, 24, 28 and 29 related to fractions and percentages. If any of these questions gave you problems, the sections on ‘Fractions’ and ‘Percentages’ in Chapter 2 should give you the information to put this right.
If questions 19, 22, 27 or 30 caused concerns, you’ll find more information in Chapter 3, ‘The SI System’.
Questions 21, 25 and 26 involved multiplying decimals. If these got you scratching your head then reading the ‘Multiplying decimals’ section in Chapter 2 should help.
If you were able to answer most of the self-assessment test questions without too much trouble, start by reading Chapter 3. This explains the SI system of measurement in more detail. Then move on to Chapter 4 that considers how to calculate drug doses and then progress to Chapter 5 on other clinical calculations. Chapter 6 will give you the opportunity to put your knowledge to the test.
KEY POINTS TO TAKE AWAY FROM THIS CHAPTER
Nurses need accurate calculation skills and a solid knowledge of numeracy for the safe administration of drugs and many other parts of their daily work.
Calculation errors are rare and can be prevented with practice and care.
There are many opportunities to develop your calculation skills during the theory and practice parts of your course.
| THIS CHAPTER: |
gives an overview of the decimal system
revises the four basic methods of calculating
considers ways of expressing and calculating numbers less than one
describes how very large numbers can be expressed.
2.1 Introduction
The modern healthcare environment demands a good understanding of decimals and the ability to use them. This includes whole numbers like 18, 140 and 567 as well as parts of whole numbers. Some medications are prescribed in whole numbers, for example paracetamol 500 mg and some are prescribed in amounts that include less than one unit, for example bendroflumethiazide 2.5 mg.
2.2 The decimal system
A number is made up from individual digits and communicates a great deal of information. If 475 is used as an example, this isn’t simply a ‘4’, a ‘7’ and a ‘5’. The place of the digit within the number gives a value such as hundreds, tens and ones. Reading from left to right 475 has a value of 4 ‘hundreds’, 7 ‘tens’ and 5 ‘ones’. This is because we use a ‘base 10’ decimal system. This means that the value of each place in a number is 10 times greater than the number to the right of it. The place value of ‘7’ is tens and of ‘5’ is ones. Similarly, the value of each place is ten times smaller than the place to its left. Figure 2.1 presents this visually.
Figure 2.1. Whole numbers and decimal fractions.
Using the example of digoxin (a drug used to control an irregular heart rate), a common dosage is 125 micrograms. The place values in the number tell us the exact amount to give: 1 ‘hundred’, 2 ‘tens’ and 5 ‘ones’ or ‘one hundred and twenty-five’ micrograms. Figure 2.2 illustrates this.
Figure 2.2. Digoxin 125 micrograms.
The decimal point is used to signpost the end of the whole number and the beginning of amounts that are less than one. Returning to the digoxin example, this can also be prescribed as 62.5 micrograms. 62.5 tells us that there are six ‘tens’, two ‘ones’ and five ‘tenths’. Figure 2.3 illustrates the positions of whole numbers and parts of whole numbers or decimal fractions.
Figure 2.3. Digoxin 62.5 micrograms.
The role of zero
Within the decimal system, zeros play an important role when there are no values. If the number 702 is used as an example, ‘7’ indicates seven hundreds, ‘0’ indicates no tens and ‘2’ indicates two ones. The ‘0’ maintains the position of the other digits within the number.
When writing numbers that contain four digits or more, you will see various different formats:
four digits – one thousand may be seen written as 1,000 (using a comma), 1 000 (using a gap) or 1000 (closed up, no gap or comma); according to the metric (SI) system, all numbers up to 9999 should be written with no space and no comma
five or more digits – ten thousand five hundred may be seen written as 10,500, 10 500 or 10500; this book again uses the SI convention and presents all numbers above 10 000 with a space.
These standards should be used in healthcare and this approach has safety advantages because the comma cannot then be mistaken for a decimal point.
ERROR ALERT
Zeros can maintain the position of other digits, but they can also be the source of errors. When calculating and giving medications or fluids, it is critical to remove any trailing zeros – ones used after the decimal point that don’t maintain the position of other digits within a number. For example, five milligrams should be written as 5 mg and not 5.0 mg. If the decimal point is not clear, the result is a ten times overdose.
Self-assessment test 2.1: digit value
The recap questions below will help to consolidate your learning about the value of digits within a number. Answers can be found at the end of the book.
1 In the number 1.65, what value does the digit ‘5’ have?
