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?
2 In the number 6.079, what value does the digit ‘0’ have?
3 In the number 8.125, what value does the digit ‘5’ have?
4 In the number 4 012 000, what value does the digit ‘4’ have?
5 In the number 12.75, what value does the digit ‘2’ have?
6 In the number 2.09, what value does the digit ‘9’ have?
7 In the number 725.3, what value does the digit ‘3’ have?
8 In the number 7.005, what value does the digit ‘5’ have?
9 In the number 0.13, what value does the digit ‘3’ have?
10 In the number 9.125, what value does the digit ‘5’ have?
2.3 Addition
Most simple additions can be performed mentally, but where many individual numbers have to be added together, like when adding up the fluid intake of a patient over twenty-four hours, the potential for error increases. In these circumstances, it is sensible to perform the calculation on paper.
The numbers are written down in a column format as in the example below. This ensures that the numbers are lined up correctly for the calculation and maintains the place value of each digit within the number. When adding two or more numbers together, the calculation can be performed in any order: 74 + 26 gives the same answer as 26 + 74.
SENSE CHECK
As well as being able to perform calculations, you need to learn ways of checking to make sure you haven’t made a careless mistake. Remember that if you add numbers together, your answer must be greater than the numbers that you started with.
Use the following procedure to check your addition answers:
take one of the numbers that you added up away from the answer
for example, 6 + 9 = 15 and therefore 15 – 9 = 6.
| EXAMPLE 2.1 |
The columns are not usually labelled as hundreds (H), tens (T) or ones (O), but this helps to illustrate the calculation.
Method
The addition is calculated vertically from right to left, starting under the ‘ones’ column and involves three individual calculations, one for the ‘ones’ column, one for the ‘tens’ column and a final calculation for the ‘hundreds’ column.
Process
This gives the answer of 7 hundreds, 7 tens and 8 ones, or 778.
Checking
To check your answer: 778 – 62 = 716.
Not all additions are this straightforward as there will be times when the calculation results in ten or more in a column, such as in Example 2.2.
| EXAMPLE 2.2 |
Method
As before,