Welcome friend!

Today we’re talking about how to master advanced dimensional analysis. And by advanced, I don’t mean hard (woo-hoo!). It’s actually easier than you might think and super simple when you use these 6 easy steps.

Building off of last months post, we are going to dive into how to use multiple conversions with dimensional analysis.

Seriously, friend, if you are not using dimensional analysis this will be a lot harder to complete. I urge you to consider switching to this method if you have not already. It just makes your life super easy peasy and stress free. Who doesn’t want that?! 🙂

Let’s dive in.

Multiple Conversions

Here’s your order:

650000mcg of Acetaminophen is to be given IV every 6 hours for pain. The 100mL bottle contains 1000mg of Acetaminophen. How many mL will the patient receive?

You can solve this in just a few easy steps: (If you want a review of these steps, check out this awesome post.)

Step 1: What do you need?

You first need to make sure you know what the question is asking for.

For this question, you need to find out how many mL the patient will receive. Write this on the right side of your paper.

Advanced Dimensional Analysis Step 1

Step 2: What is ordered?

650000mcg is ordered to be given every 6 hours. Write this on the left side of your paper.

Advanced Dimensional Analysis Step 2 (1)

Step 3: What are your available conversions?

The question gives you one conversion: the 100mL bottle contains 1000mg of Acetaminophen. Write that conversion in the middle of your paper.

But there is another conversion you need: converting micrograms (mcg) to milligrams (mg).

Not sure how to convert that? NO PROBLEM! Of course, we have a cheat sheet for that!

Submit your name and email to download your FREE Dosage Calculation Conversions Cheat Sheet so you never forget a conversion factor again!


There are 1000mcg in 1mg. So you will write that conversion in the middle of the paper as well.

Advanced Dimensional Analysis Step 3 (1)

Step 4: Solve the problem.

Multiply across the top. Multiply across the bottom. And divide the two. It’s that simple! I hope you’re loving dimensional analysis as much as I am right now!

Advanced Dimensional Analysis Step 4

Step 5: Round appropriately

Your answer is a whole number, so rounding rules do not apply here. And make sure you don’t add any trailing zeros. Why? Because 65.0 can look a lot like 650 if that decimal gets lost. Yikes!

The answer is simply 65mL.

Step 6: Check your answer.

Complete the problem again using the same steps, just to be sure. It never hurts to double check, but it might hurt not to.

And viola! You’re a dimensional analysis and dosage calculation PRO! Are you convinced now that dimensional analysis is the best thing ever? I thought so! 🙂

See you on the other side of your exam, my friend. Until then, stay cool.