Proportional Analysis versus Dimensional Analysis - Most Difficult Example

A 55 pound patient is prescribed 5 mg/kg/day of diphenhydramine HCl.  The daily dose it to be divided into 4 doses, each administered 6 hours apart.  Available medication is a 12.5 mg/5 mL solution.  How many teaspoons need to be given to the child at one time.

By Proportion Analysis

By Dimensional Analysis

Discussion: The proportion analysis technique setting requires up, cross-multiplying, and solving for the unknown variable 4 separate times.  In the end the student nurse must remember “10 tsp” is a full day’s dose, not the amount given every 6 hours.  To get the final answer the “10 tsp” should be divided by 4 (a 5^th proportion could have been set up to arrive at the same result).  Intermediate results introduce the risk of inappropriate rounding—not the case in this specific example because intermediate results were whole numbers—that may introduce significant error into the final calculation.  With the dimensional analysis technique a single equation is set up and all intermediate results are automatically held in the calculator’s memory to at least 8 decimal places so that a chance for error is eliminated.  Also, a final ratio does not need to be set up, as with the proportion analysis technique.  Instead a single universal approach is used.