The following outline can be used as a guide for doing dimensional analysis (DA). Some familiarity with DA is assumed. See the 25 Med-math Problems Solved for an introduction to DA. While not all steps listed below will be needed to solve all problems, I have found that any problem that can be solved using DA will yield its answer if the following steps are followed. I would not suggest memorizing the sequence of steps, but rather understanding and practicing them. Understanding is more durable than memory.

1. Determine what you **want** to know. Read the problem and identify what you're being asked to figure

out, e.g. "how many milligrams are in a liter of solution."

a. **Rephrase** if necessary using "per." Example: You want to know "milligrams per liter."

b. **Translate** into "math terms" using appropriate abbreviations to end up with "mg/L" as your answer

unit (AU). Write this down, e.g. "AU= mg/L"

2. Determine what you already **know**.

a. What are you **given** by the problem, if anything? Example: "In one minute, you counted 45 drops."

• **Rephrase** if necessary. Think: "Drip rate is 45 drops **per** minute."

**• Translate** into math terms using abbreviations, e.g. "45 gtt/min"

— If a given is in the form mg/kg/day, rewrite as mg/kg x day.

— If a percentage is given, e.g. 25%, rewrite as 25/100 with appropriate labels.

b. Determine **conversion factors** that may be needed and write them in a form you can use, such as

"60 min/1 hour." You will need enough to form a "bridge" to your answer unit(s).

• Factors known from memory: You may know that 1 kg = 2.2 lb, so write down "1 kg/2.2 lb"

and/or "2.2 lb/1 kg" as conversion factors you may need.

• Factors from a conversion table: If the table says "to convert from lb to kg multiply by 2.2," then

write down "2.2 lb/1 kg"

3.** Setup** the problem using only what you need to know.

a. Pick a **starting factor**.

• If possible, pick from what you know a factor having one of the units that's also in your answer

unit and that's in the right place.

• Or pick a factor that is given, such as what the physician ordered.

• Note that the starting factor will always have at least one unit not in the desired answer unit(s) that

will need to be changed by canceling it out.

b. Pick from what you know a conversion factor that cancels out a unit in the starting factor that you

don't want.

c. Keep picking from what you know factors that cancel out units you don't want until you end up with

only the units (answer units) you do want.

d. If you can't get to what you want, try picking a different starting factor, or checking for a needed

conversion factor.

e. If an intermediate result must be rounded to a whole number, such as drops/dose which can only be

administered in whole drops, setup as a separate sub-problem, solve, then use the rounded off

answer as a new starting factor.

4. **Solve**: Make sure all the units other than the answer units cancel out, then do the math.

a. Simplify the numbers by cancellation. If the same number is on the top and bottom, cancel them out.

b. Multiply all the top numbers together, then divide into that number all the bottom numbers.

c. Double check to make sure you didn't press a wrong calculator key by dividing the first top number

by the first bottom number, alternating until finished, then comparing the answer to the first one.

Miskeying is a significant source of error, so always double check.

d. Round off the calculated answer.

• Be realistic. If you round off 74.733333 to 74.73 mL that implies that all measurements were of

an extreme accuracy and that the answer is known to fall between 74.725 and 74.735, or 74.73

__+__ 0.005 mL. A more realistic answer would probably be 74.7 mL or 75 mL. See example 6.

• If you round to a whole number that implies a greater accuracy than is appropriate, write your

answer to indicate a range, such as 75 __+__ 5 mL.

e. Add labels (the answer unit) to the appropriately rounded number to get your answer. Compare

units in answer to answer units recorded from first step.

5. Take a few seconds and **ask yourself if the answer you came up with makes sense**. If it doesn't,

start over.

This is a fairly bare outline. The steps are best *taught*, rather than *read*, and so would serve better as a guide to tutoring students than as a self-teaching guide.

A copy of the above guide in Word format is available, click here.

## A Briefer Summary

• Don't panic. Break THE PROBLEM down into small ones you CAN solve.

• Figure out what answer unit(s) you **want** to end up with. This is usually easy.

• Write down, in math terms, everything you **know** that relates to the problem. You may need to read the problem several times,
rephrasing parts of it, so you can translate everything into math terms. You
may need to look up a few conversion factors, but that's inconvenient, not
difficult.

• You now **need** to pick a starting factor. If possible pick one that already has one of the
units you want in the right place. Otherwise start with something you are given
that is not a conversion factor.

• Plug in conversion factors that allow you to cancel out any units you don't
want until you are left with only the units you do want (your answer units).

• If you can't solve the problem, pick a different starting factor and start
over.

• Do the math and **solve ** it. Now double-check your calculations.

• Ask yourself if the answer seems right or reasonable. If not, recheck
everything.

Support this site: Visit our Zazzle store featuring ultra hi-res images of artworks, Hubble/ESA/NASA space images, Mandelbrot fractals, maps and more. Images up to 525 megapixels allow for fine printing at the largest sizes. Give a fine print as a gift that could hang around for a hundred years.

### Other sites by Alysion

- World's Funniest Jokes
- Survival Retreat? Maybe now is the time
- For wisdom: follow The Path of the Dog
- Beginnings: First Lines from Scriptures
- World Religions Simplified
- Buyer's Guide to Food Preparedness Products
- One Homestead: An intentional community
- Poems to Memorize & Memorable Poems
- Mom's Favorite Poems
- Ryan's Favorite Poems
- WWW Collection of Favorite String Figures
- Take the Super Post-Mensa IQ Test
- Alternative Handwriting and Shorthand Systems
- Handywrite
- Handywrite Shorthand
- Making the Tree of Life: Fun with phylogenetics
- Human Chow: The Website
- Small Animal Euthanasia at Home
- Fun with Dimensional Analysis
- Making Boxes for your Rock & Mineral Collection
- Making a Mass Balance Scale
- Ryan's 50 States Flashcards
- Adventures of MeraLee
- World Religions Simplified
- eBike Touring Association
- The True Right to Life Movement
- Walled-in: A poem
- Cochise Stronghold Trail

### External Links

- Fun with Dimensional Analysis
- For everyone else.

- Math Skills Review
- For chemistry students.

### Top 10 Poems from Alysion's

### Bucket List of Poems

to Read Before You Die

- 1. The Rainy Day by Henry W. Longfellow
- 2. Fire and Ice by Robert Frost
- 3. A Dream within a Dream by Edgar Allan Poe
- 4. The Purple Cow by Gelett Burgess
- 5. If by Rudyard Kipling
- 6. To See a World by William Blake
- 7. Ten Little Limericks
- 8. First Fig by Edna St. Vincent Millay
- 9. Alone by Edgar Allan Poe
- 10. I'm nobody! Who are you? Emily Dickinson

One of many How-to videos on YouTube.