# Welcome to SMIRK Unit
9 - Calculating drug
dosage

- Introduction
- Applying a formula
- Working out the dosage
- The next step
- What is rounding up?
- Quick quiz
- Answers
- Back to main index

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SMIRK - Calculating dosage by Gill Lngmack and Caroline Burton, University of Nottingham modified by Marion Kelt, Glasgow Caledonian University is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at http://find.jorum.ac.uk/resources/396.

# Introduction

Calculating correct medication dosages is an essential skill within all medical and related disciplines. Patients need accurate dosages of prescribed medicines to fulfil their treatment regimes. One problem is that children do not come in a standard size and so need only a part of a vial rather than all of it.

#### The Importance of Calculations

Before starting to measure out the medicine and preparing to give it, the medicine needs to be calculated precisely. 1ml syringes have graduations of 0.01 to 0.99, so medicines less than 1ml need to be calculated to 2 decimal places. 2.5ml, 5ml, and 10ml syringes have graduations of 0.1ml so need to be calculated to 1 decimal place.

#### Rounding decimals up and down

To be accurate, medicines need to be calculated to one decimal place beyond that required in order to round the value up (if the 2nd decimal place is 5 or over) or down (if the 2nd decimal place is less than 5).

In a 1ml syringe, the value required would need to be calculated to 3 decimal places in order to round up or down as appropriate.

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SMIRK - Calculating dosage by Gill Lngmack and Caroline Burton, University of Nottingham modified by Marion Kelt, Glasgow Caledonian University is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at http://find.jorum.ac.uk/resources/396

# Applying a formula

To accurately calculate medicine dosage, a simple formula is used: what you want over what you've got times what it's in. This can be used for most applications. Applying a formula to calculate the exact amount required is particularly useful when calculating liquid medicines (elixirs or suspensions) or the amount of injection required.

#### Scenario

Claire, a 4 year old child, weighs 18kg. She is prescribed a dose of 180mg Paracetamol in response to the formulary suggestion of 10mg to 15mg per kg. The formula can be used to calculate exactly the amount of medicine Claire requires.

The next pages show how to work out the dosage you need.

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SMIRK - Calculating dosage by Gill Lngmack and Caroline Burton, University of Nottingham modified by Marion Kelt, Glasgow Caledonian University is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at http://find.jorum.ac.uk/resources/396

# Working out the dosage

#### Step 1: Developing the formula to be calculated

Claire requires 180mg of Paracetamol. The solution in the elixir contains 120mg of Paracetamol in 5mls of solution.

#### Step 2: Working out the fractions in the equation

Simplify the parts of the fraction to the smallest whole numbers. This makes the equation easier to work out. Remember that whatever you do to the top of the equation you must also do to the bottom of the equation.

Within this equation, you can divide 180 by 10, then 120 by 10, which leaves 18 over 12.

Then you can simplify again by dividing the top and bottom by 6 which leaves 3 over 2, or:

180 | divided | 18 | divide again | 3
----- | by 10 | ---- | by 6 | ---
120 | equals | 12 | equals | 2

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SMIRK - Calculating dosage by Gill Lngmack and Caroline Burton, University of Nottingham modified by Marion Kelt, Glasgow Caledonian University is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at http://find.jorum.ac.uk/resources/396

# The next step

#### Step 3: Calculating how much medicine Claire requires

The final simplified equation can be easily calculated.

3 times 5 (the amount of solution) equals 15 over 2.

3 |  | 5 |  | 15
--- | times |  | equals | -----
2 |  |  |  | 2

15 divided by 2 equals 7 with 1 remaining. By extending beyond the decimal point and using a nought, 2 divides into 10 5 times.

Therefore Claire needs 7.5mls of Paracetamol.

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SMIRK - Calculating dosage by Gill Lngmack and Caroline Burton, University of Nottingham modified by Marion Kelt, Glasgow Caledonian University is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at http://find.jorum.ac.uk/resources/396

# What is rounding up?

Some decimal numbers go on for ever! To simplify their use, we decide on a cut off point and “round” them up or down.
If we want to round 2.734216 to two decimal places, we look at the number in the third place after the decimal, in this case, 4. If the number is 0, 1, 2, 3 or 4, we leave the last figure before the cut off as it is. If the number is 5, 6, 7, 8 or 9 we “round up” the last figure before the cut off by one. 2.734216 therefore becomes 2.73 when rounded to 2 decimal places.
If we are rounding to 2 decimal places, we leave 2 numbers to the right of the decimal.
If we are rounding to 2 significant figures, we leave two numbers, whether they are decimals or not.

Rounding up should only be done at the final stage of your calculation. Rounding up midway through can throw out the final result!

Example:

2 | 4 | 3 | .7 | 6 | 8 | 4 | = | 243.77 (two decimal places)
|  |  |  |  |  |  | = | 240 (two siginificant figures)

1 | 9 | 7 | 3 | . | 2 | 8 | 5 | = 1973.29 (2 decimal places)
|  |  |  |  |  |  |  | = 2000 (2 siginificant figures)

2 | . | 4 | 6 | 8 | 9 | = | 2.47 (two decimal places)
|  |  |  |  |  | = | 2.5 (two siginificant figures)

0 | . | 9 | 9 | 8 | 7 | 9 | = | 1.00 (2 decimal places)
|  |  |  |  |  |  | = | 1.0 (2 significant figures)

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SMIRK - Calculating drug dosage by Tom Frank, Eric Williams and Clare Wright, University of Birmingham Careers Centre adapted by Marion Kelt Glasgow Caledonian University is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

# Quick quiz

Try these examples. Give all your answers to 2 decimal places and 2 significant figures
1. 2.45 + 7.68 | 2. 3.17 + 12.15 | 3. 2.421 + 13.1
4. 162.5 + 2.173 | 5. 12.5 – 3.7 | 6. 9.6 – 7.8
7. 163.5 – 2.173 | 8. 2.416 – 1.4 | 9. 26.95 – 1.273
10. 1.5 x 7.2 | 11. 2.73 x 8.14 | 12. 6.25 x 17 x 3
13. 2.96 x 17.3 | 14. 4.2 / 1.7 | 15. 53.9 / 2.76
16. 14.2 / 6.1 | 17. 2.5 / 0.03 | 18. 250/2.35

That is the end of our section on calculating dosage. More help is available from your Learning Development Centre.

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SMIRK - Calculating drug dosage by Tom Frank, Eric Williams and Clare Wright, University of Birmingham Careers Centre adapted by Marion Kelt Glasgow Caledonian University is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

# Answers

Question | 2 decimal places | 2 significant figures
--- | --- | ---
1 | 10.13 | 10
2 | 15.32 | 15
3 | 15.52 | 16
4 | 164.67 | 160
5 | 8.80 | 8.8
6 | 1.80 | 1.8
7 | 161.33 | 160
8 | 1.02 | 1.0
9 | 25.68 | 26
10 | 10.80 | 11
11 | 22.22 | 22
12 | 318.75 | 320
13 | 51.21 | 51
14 | 2.47 | 2.5
15 | 19.53 | 20
16 | 2.33 | 2.3
17 | 83.33 | 83
18 | 106.38 | 110

That is the end of our section on calculating dosage. More help is available from your Learning Development Centre.

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SMIRK - Idea generation or ideation by Bernard Leong, Lee Iwan and Litemind blog modified by Marion Kelt, Glasgow Caledonian University is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at http://www.slideshare.net/bleongcw/7-tips-for-idea-generation-for-startups and http://leeiwan.wordpress.com/2006/08/28/5-ways-to-promote-creative-thinking-and-idea-generation/ and http://litemind.com/6-tips-generate-outstanding-ideas/.