Using numbers and handling data

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# 1.5 Rounding to decimal places

Sometimes the result of a calculation gives a number with lots of decimal places - far more than you need or could reliably measure. For instance, suppose a patient is required to receive 5 ml of medicine a day, evenly spaced in three injections. How much medicine should they be given in each dose?

To divide the 5 ml of medicine into three equal parts would mean measuring out 5 ÷ 3 = 1.6666 ml (where the 6s keep repeating, or recurring indefinitely). It's not realistic or feasible to measure out the medicine to this kind of accuracy. Instead, you first need to think about what level of accuracy is needed. An injection of this volume would be most accurately dispensed using a 2 ml syringe, marked in 0.1 ml increments. In this case then, the accuracy of your measurement would be limited to 0.1 ml, or in other words to one decimal place. To administer the amount calculated above you would need to round the figure to the nearest decimal place.

The rule to remember with rounding to a particular decimal place is that if the next number to the right of that decimal place is 5 or more, you round the figure up to the next highest number, and if it's 4 or less it remains the same. For instance, to correct 1.6666 ml to one decimal place, find the first decimal place and then look at the next (smaller) decimal place to its right, which we've highlighted here as 1.6666 ml. As this number is greater than 5 we have to round up, and the amount becomes 1.7 ml corrected to one decimal place (1 dp). If the original number had been 1.6466 ml then the value corrected to one decimal place would be 1.6 ml (1 dp).

Here are some more worked examples for you to practise with:

Now try rounding numbers to specific decimal places for yourself with practice question 9.

Right click and open the practice questions [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] in a separate window, then you can switch easily between the course text and the questions.

## Box 1 General rules for numbers in healthcare

• Try to avoid the need for a decimal point

• Use 500 mg not 0.5 g

• Use 125 mcg not 0.125 mg

• Never leave a decimal point 'naked'

• Paracetamol 0.5 mg not Paracetamol .5 mg

• Avoid using a terminal zero

• Diazepam 2 mg not Diazepam 2.0 mg

• Put a space between the drug name and dose

• Apresoline 55 mg not Apresoline55 mg

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