Advice from the experts
Quick Guide to Dimensional Analysis
Need to calculate a dosage? Need to figure out a drip rate? Don't panic! Just follow this step-by-step guide to dimensional analysis to come up with the number you need quickly and accurately.
Step 1: Given
Identify the given quantity in the problem. This is what the problem already gives you! Get it?
Step 2: Wanted
Identify the wanted quantity in the problem (the unknown unit, or the answer to the problem, or what you need).
Step 3: Conversion factor
Write down the equivalents that are necessary to convert between systems. Remember, conversion factors can convert to either fraction you need. Depending on what your wanted quantity in your numerator is, you can decide which conversation factor fraction to use.
Step 4: The problem
Set up the fractions so that the units you need to cancel appear as both a numerator and a denominator. Units can't be cancelled if they appear only as numerators or only as denominators.
Step 5: Unwanted units
Cancel unwanted units that appear in the numerator and denominator to isolate the unit you're seeking for the answer.
Step 6: Multiply, multiply, and divide
This is where you use math to solve the problem. Multiply the numerators, multiply the denominators, and divide the products.
Fun with dimensional analysis!
Now try this sample problem using the steps identified above.
A doctor prescribes 75 mg of a drug. The pharmacy stocks a solution containing the drug at a concentration of 100 mg/mL. What dose should you give in milliliters?
Step 1: Given = 75 mg
Step 2: Wanted = X mL
Step 3: Conversion factor: 100 mg = 1 mL
Step 4: Set up the equation (Remember that units you want cancelled should be positioned in both a numerator and a denominator.):
Step 5: Cancel unwanted units:
Step 6: Multiply, multiply, and divide:
More fun!
Here's one more:
The doctor prescribes 250 mg of amoxicillin (Amoxil), which comes in a suspension of 25 mg/mL. You need to give the dose in teaspoons (tsp). How many teaspoons of the suspension should you give?
Step 1: Given = 250 mg
Step 2: Wanted = X tsp
Step 3: Conversion factors (Remember, some conversion factors you should know by memory, such as 1 tsp = 5 mL.): 25 mg = 1 mL; 1 tsp = 5 mL
Step 4: Set up the equation:
Step 5: Cancel unwanted units:
Step 6: Multiply, multiply, and divide:
