A guide to dimensional analysis for nursing students.

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.

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One of many How-to videos on YouTube.

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