1. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Chapter 11 Dimensional Analysis

2. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Dimensional Analysis Used in mathematics and science Simpler and more accurate

3. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Steps to Setting Up a Dimensional Analysis Problem Identify the desired dose. Place it in the numerator. Identify the supply or available dose. Identify what you are solving for (this is stated in the problem). Draw a circle around this measurement system. Combine steps 1 and 2. Set up the problem so that the measurement systems you do not need for the answer cancel each other. This should leave the measurement system desired on the top of the equation.

4. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Steps to Setting Up a Dimensional Analysis Problem (cont.) If possible, reduce the fraction. Cancel any like measurement systems. Multiply the numbers in the numerator. Multiply the numbers in the denominator. Divide the numerator by the denominator.

5. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Dosage Calculations D = Desired dose or order H = On hand or have S = Supply

6. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Formula O × H = x S Set up problem with numerator and denominator and then solve the problem

7. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Question Order: Zyprexa (olanzapine) 10 mg po every day Supply: Zyprexa (olanzapine) 5 mg scored tablets How many tablets will you administer? A. ½ B. 1 C. 1½ D. 2

8. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Answer D. 2 10 mg × 1 tablet/5 mg = 2 tablets

9. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Medication Equation and Calculation O × H = x S Set up problem with numerator and denominator and then solve the problem Use the same equation for –Oral solid and liquid medications –Parenteral liquid medications

10. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Conversion Factor Term used in dimensional analysis that means the equivalents necessary to convert between systems of measurement. Conversion factor is a ratio of units that equals 1.

11. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Dimensional Analysis Method With Equivalency Conversions Identify the desired dose. Place it in the numerator. Identify the supply or available dose. Identify what you are solving for (this is stated in the problem). Draw a circle around this measurement system. Identify any conversions needed. Add the conversion factors to the equation. Add these to the equation so that like measurement systems will cancel each other.

12. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Dimensional Analysis Method With Equivalency Conversions (cont.) Combine steps 1 and 2. Set up the problem so that the measurement systems that you do not need for the answer will cancel each other. This should leave the measurement system desired on the top of the equation. If possible, reduce the fraction. Cancel any like measurement systems. Multiply the numbers in the numerator. Multiply the numbers in the denominator. Divide the numerator by the denominator.

13. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Sample Problem Order: Motrin (ibuprofen) 0.6 gram po bid Supply: Motrin (ibuprofen) 400 mg tablets How many tablets will be administered?

14. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Sample Problem Answer O × conversion factor x H = x S 0.6 gram × 1000 mg/1 gram × tablet/400 mg = 1½ tablets

15. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Dimensional Analysis Method With Weight-Based Calculations Medications calculated on the basis of weight will add a further step of the ordered dose being multiplied by the weight or BSA

16. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Sample Dimensional Analysis Method With Weight-Based Calculations Order: Lasix (furosemide) 2 mg/kg IV bid for a patient weighing 60 kg Supply: Lasix (furosemide) 10 mg/mL 2 mg/1 kg × 1 mL/10 mL x 60 kg = 12 mL

17. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Sample Dimensional Analysis Method With Calculation of Intravenous Fluids Order: NS 1000 mL over 8 hours Supply: Drop factor 10 gtt/mL 1000 mL/8 hour × 10 gtt/mL × 1 hr/60 min = 20.8 or 21 gtt/min

18. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Question Order: NS 1000 mL over 6 hours Supply: Drop factor 15 gtt/mL How many gtts/min? A. 41 B. 42 C. 43 D. 44

19. Copyright © 2009 Wolters Kluwer Health | Lippincott Williams & Wilkins Answer B. 42 1000 mL/6 hours × 15 gtt/mL × 1 hour/60 min = 41.6 = 42 gtt/min