Dimensional Analysis

Dimensional Analysis

Veterinary Science

Dimensional Analysis can also be called the Unit Factor Method or the Label Method.

It's a way of converting through different types of measurement to end up with what is needed.

Consider the following problem: A cat weighing 11 lbs requires an antibiotic at a dose of 15 mg/kg. The antibiotic comes in a concentration of 125 mg/5mL. How many mL do you give?

Here we have to go from lbs to kg then we need to figure mg/kg then mg/mL. This requires multiple conversions. Here's where Dimensional Analysis comes in handy!

Let's start with a YouTube clip.....

Let's do a fun one!!! Here we need the conversion factor for:

1. Students per class

2. Slices per student

3. Slices in each pizza

4. Price per pizza

Here are the conversion factors!

Notice that every segment is equal. 25 Students = 1 class. 2 slices = 1 student. 1 pizza = 5 slices. $10.00 = 1 pizza.

Cross out the units that match but leave the numerical values.

• Students

• Slices

• Pizza

Multiply and divide the numerical values left.

• Multiply 25 x 2 x 1 x 10 = 500

• Multiply 1 x 1 x 5 x 1 = 5

• Then divide  $500\div5\ =$  100

•  $\frac{100\ dollars}{1\ class}$  

Our final answer is $100 to feed the entire class.

Let's look back at our initial problem again:

A cat weighing 11 lbs requires an antibiotic at a dose of 15 mg/kg. The antibiotic comes in a concentration of 125 mg/5mL. How many mL do you give?

Set up the problem with the conversion factors:

11 lbs = 1 cat. 1 kg = 2.2 lbs. 15 mg = 1 kg. 5 mL = 125 mg.

Cross off the units that cancel out.

• lbs

• kg

• mg

Multiply across then divide

•  $11\times1\times15\times5=825$  

•  $1\times2.2\times1\times125=275$  

•  $\frac{825}{275}=3$  

Our answer is 3 mL

Let's try one more!

A cat weighing 4.5 kg needs insulin at 1.5 international units (IU) per kg. The insulin comes in a strength of 10 IU per mL. How much insulin do you give? (answer to nearest tenth of a mL)

Find the conversion factors and set up the problem.

Here is our problem!

4.5 kg = 1 cat. 1.5 IU = 1 kg. 1 mL = 10 IU.

Cross off the units that cancel each other out. Leave the numerical value.

Multiply across then end with division.

•  $4.5\times1.5\times1=6.75$  

•  $1\times1\times10=10$  

•  $\frac{6.75}{10}=0.675$  

0.675 rounded to the nearest tenth is 0.7

Our answer is 0.7 mL

YOU CAN DO IT!!!!!