1. Pharmaceutical Calculations: The International System of Units
Danielle DelVillano, Pharm.D.

2. Objectives
Demonstrate an understanding of the International System of Units
Convert measures within the International System of Units
State equivalent measures and complete conversions between the International System of Units and other systems of measure used in pharmacy
Apply the International System of Units correctly in calculations

3. Introduction International System of Units (SI)
Formerly called metric system
Base units
Meter
Kilogram
Liter

4. Guidelines for Correct Use
Two symbols for microgram
mcg μg
Decimals are used, not fractions
5.25 mg
NOT 5 ¼ mg
Leading zero should be used before all decimals
0.5 mg
NOT .5 mg
Trailing zeros should not be placed after whole numbers
5 mg
NOT 5.0 mg

5. Common Conversions Length Volume Weight 1 m = 100 cm 100 cm = 1000 mm
1 L = 1000 mL
Weight
1 g = 1000 mg
1 g = kg
1 mg = 1000 mcg

6. Useful Equivalents
Ansel, H. C. (2009) Phamaceutical Calculations (13th Ed.). Philadelphia:Lippincott Williams & Wilkins, and Wolters Kluwer Publishers

7. Practice Problem 1: Reducing SI Units
By decimal shift
Reduce 9876 milligrams to grams
To convert from smaller to larger number shift the decimal RIGHT
9876 mg = g
Reduce liters to microliters
To convert from larger to smaller number shift the decimal LEFT
2.525 L = 2525 mL = 2,525,000 μL

8. Practice Problem 2: Reducing SI Units
Reduce 85 micrometers to centimeters
By ratio and proportion: (KNOW 1 cm = μm)
1 cm = x cm
10000 mcg mcg
(85 mcg)(1 cm) = x cm
(10000 mcg)
x = cm

9. Practice Problem 2: Reducing SI Units
Reduce 85 micrometers to centimeters
By dimensional analysis: (KNOW 1 cm = μm)
85 μm X cm__ = cm
10000 μm

10. Practice Problem 3: Addition
Reduce to common denomination then add or subtract
Add 1 kg, 250 mg, and 7.5 g
1 kg = 1000 g
250 mg = 0.25 g g
0.25 g g g

11. Practice Problem 4: Subtraction
Reduce to common denomination then add or subtract
Subtract 2.5 mg from 4.85 g
2.5 mg = mg g g g

12. Practice Problem 5: Multiplication
Multiply 820 mL by 12.5 and express the result in liters
820 mL
x _
10250 mL
10250 mL = L

13. Practice Problem 6: Division
Divide g by 15 and express the result in milligrams
0.465 g
÷ __
0.031 g
0.031 g = 31 mg

14. Questions

15. Reference
Ansel, H. C. (2009) Phamaceutical Calculations (13th Ed.). Philadelphia:Lippincott Williams & Wilkins, and Wolters Kluwer Publishers

16. Additional Problems

17. Chapter 2 Problem 2 Add 7.25 L and 875 cL. Reduce the result to mL.

18. Chapter 2 Problem 8
A liquid contains 0.25 mg of a substance per milliliter. How many grams of the substance will 3.5 L contain?
0.875 g

19. Chapter 2 Problem 13
Aspirin tablets generally contain 325 mg of aspirin. How many such tablets may be prepared from the 5 kg of aspirin?
15,384 tablets

20. Chapter 2 Problem 15
Norgestrel and ethinyl estradiol tablets are available containing 0.5 mg of norgestrel and 50 mcg of ethinyl estradiol. How many grams of each ingredient would be used in making 10,000 tablets?
5 g norgestrel
0.5 g ethinyl estradiol

21. Chapter 2 Problem 20
A patient is instructed to take three 50 mcg tablets of pergolide mesylate (PERMAX) daily. How many mg of the drug would the patient receive weekly?
1.05 mg pergolide mesylate

22. Chapter 2 Problem 31
A prefilled syringe contains 20 mg of a drug in 2 mL of solution. How many micrograms of drug would be administered by an injection of 0.5 mL of the solution?
5000 mcg

23. Chapter 2 Problem 38
If an albuterol inhaler contains 18 mg of albuterol, how many inhalation doses can be delivered if each inhalation dose contains 90 mcg?
200 doses

24. Chapter 2 Problem 49
The product of biotechnology, filgrastim (NEUPOGEN), is available in vials containing 0.3 mg of drug in each milliliter. Which choice is equivalent in concentration? (a) 0.03 mg/0.1 dL (b) 300 mcg/0.01 dL
(c) 3 mcg/0.01 cL
(d) 300 mcg/10 cL
(b) 300 mcg/0.01 dL