Dimensional AnalysisYour Friend not your Enemy!

The First Thing You Always Ask

Yourself is:

• What is the question asking me to find? What is the unknown piece? What is/are the unit/s of measure that need to be calculated?

Example: If the question stated, “The physician has ordered Wellbutrin 75 mg po for smoking cessation. The medication is supplied in 150 mg tablets. How many tablets will the nurse administer?

• What item is the question asking you to identify in the question above?

• Answer: How many tablets. Good Job!

Try it AgainHow many inches are in 2 feet?

What is the unknown piece of information?

Answer: inches (in two feet) Good Job!

Were these easy?

• Unfortunately they are not all that easy

• The question may require several steps

before a final answer can be formulated.

• Many students get confused because they

see a lot of numbers and words in the

sentence: e.g. 75mg, 150mg, po, tid, in 24

hours, physician, nurse, tablets, kg etc…

• If you can stay focused on what the ultimate

goal or variable is that you want to pull from

the sentence then you usually won’t go

astray

HERE’S AN EXAMPLE OF

DISTRACTERS

• A patient weighed 80 kg on admission and is now 75 kg. The

doctor’s order states that they are to receive 50mg of Drug X

mixed in 250mL of Normal Saline every 8 hours. How many

mg will the patient receive at 3pm, which is when the next

dose is due?

• What is the question asking? What item/piece of

information needs to be extracted from the question?

• Answer: Good Job if you said “How many milligrams at

next dose”

• What is the answer?

• Answer: 50mg

Did we need to know about:A patient weighed 80 kg on admission and is

now 75 kg. The doctor’s order states that they are

to receive 50mg of Drug X mixed in 250ml of

Normal Saline every 8 hours for 24 hours. How

many mg will the patient receive at 3pm, which is when the next dose is due?

Try It Again With A Little

Less Information

Dr. Orders: Demerol 50 mg IM STAT

Available: Demerol 100mg/2mLWhat is the piece of information that you

must find?

Answer: Good Job if you said “How

many mL”

See if you can get this one

What is the statement asking you to find?

The physician has ordered heparin IV drip at 1200 units per hour. The medication is supplied in 25,000 units/500mL of NS. Calculate the flow rate in mL/hr.

Answer: How many mL it must infuse in one

hour

Dimensional Analysis

Similar to Ratio and Proportion in that you:

• deal with fractions

• deal with known and unknowns

• must set it up a certain way

Now that we know what to retrieve we are

ready to set up the problem!

• Sometimes the answer can be easily

retrieved without any written computation.

• Can you give the answer to this question

without writing it down?

“ The physician has ordered Wellbutrin 200 mg

p.o. for smoking cessation. The medication is

supplied in 100 mg tablets. How many tablets

will the nurse administer?

• Answer: 2 tablets Good Job! Let’s work

it out using dimensional analysis.

1. The physician has ordered Wellbutrin 200 mg p.o.

for smoking cessation. The medication is supplied in

100 mg tablets. How many tablets will the nurse

administer?

The Item: How many tablets

Write it down the same way ? Tablets

What ever the item is, whether it is tablets, mg,

kg, mL, hours etc.. You always write it first and

write it as a numerator (e.g. tablets)

X

2.

Then return to your statement and pull

everything from it that deals with your

item (the tablets).

The physician has ordered Wellbutrin 200

mg p.o. for smoking cessation. The

medication is supplied in 100 mg tablets. How many tablets will the nurse administer?

1 tablet = 100mg

This is the concentration of the medication you

have available to you.

3.

? tablets 1 tablet

dose = 100mg

The physician has ordered Wellbutrin 200 mg

p.o. for smoking cessation. The medication is

supplied in 100 mg tablets. How many tablets will the nurse administer?

4. Cross elimination-

- Although you will need some of the other numbers in

the statement in order to produce your answer- the

words attached to those numbers have to be

eliminated.(i.e. in this case mg.)

- The only way to do this is to align them so that you can

cross eliminate. You keep the #’s but get rid of the title

? Tablets = 1tablet x 200mg

dose 100mg dose

- Multiply the concentration (100mg/tablet) and the

ordered dose (200mg/dose) to get the # of tablets

required.

5.? Tablets = 1tablet x 200mg

dose 100mg dose

You got rid of the mg and the only thing left is

what you needed- tablets.

Now multiply across

?tablets = 1 tablet x 200mg= 200

dose 100mg dose 100

Now Divide 200 = 2 tablets

100

There is always another item to know!

Conversions!

Conversions

• Quite often the numbers provided in the statement are in a unit of measure different from the question

• For e.g. you are asked how many kg the patient weighs when all you have in the statement is the weight in pounds, or a drug is stated in grams and you must give milligrams

• Example: The physician orders 0.4mg of atropine. The drug label reads 400mcg per 1mL

• Going back to our 1st step- what is the piece of information we need to find?

• Answer: how many mL?

Conversions• You must memorize several important

conversions or know when and where to

look them up!!!

• They will be a very important step in you

completing many problems

1 gm = 1000 mg 1 mg = 1000 mcg 1 gm = 1,000,000 mcg

1 L = 1000 mL 1 oz = 30 mL 1 tsp = 5 mL

1lb = 16 oz 1 kg = 2.2 lbs 1 kg = 1000 gm

1 gm = 1000 mg 1 mg = 1000 mcg 1 gm = 1,000,000 mcg

1 L = 1000 mL 1 oz = 30 mL 1 tsp = 5 mL

1lb = 16 oz 1 kg = 2.2 lbs 1 kg = 1000 gm

Looking at the table, which conversion equation do you think

we need in order to complete our problem: “ The Physician

orders 0.4 mg of atropine. The drug label reads 400mcg/mL. How many mL will you administer?

Answer: You need a conversion that has both mg and mcg. So you would choose 1 mg= 1000mcg

? mL = 1mL x 1000mcg x 0.4 mg = 400 = 1mL

Dose 400mcg 1mg dose 400 dose

Try this one yourself.

•The physician has ordered heparin IV drip at 1200 units per hour. The medication is supplied in 25,000 units/500 mL of NS. Calculate the flow rate in mL/hr. __________

•ANS: 24 mL/hr