[latexpage]

When tablets are prescribed for a patient, the dosage of the tablets supplied is often different from the prescription, and nurses must calculate the number of tablets to administer. Dimensional analysis can be used to calculate the number of tablets to administer. Let’s practice using dimensional analysis using a practice problem.

Practice Problem: Tablet Dosage

Jane Doe recently had her prescription changed by her provider from Carvedilol 6.25 mg twice daily to Carvedilol 25 mg once daily. Jane shows you her prescription bottle (see Figure 5.7^[1]) and asks, “How many pills can I take every day so I can use up what I have before purchasing another refill?” How many 6.25 mg tablets will you instruct Jane to take based on the new prescribed dose of Carvedilol 25 mg once daily?

Solve this question by using dimensional analysis.

1. Start by identifying the goal unit for which you are solving, which is a tablet (tab) in this scenario:

\[

{Tab}~=

\]

2. Set up the first fraction with tab in the numerator to match the goal unit. From the prescription bottle, we know that one of the supplied tablets has a concentration of 6.25 mg, so place 1 in the numerator and 6.25 mg in the denominator:

\[

{Tab}~=~\frac{1~tab}{6.25~mg}

\]

3. Set up the second fraction with the intent to cross out mg, so place mg in the numerator. By reviewing the prescription, we know the new dosage prescribed is 25 mg, so place 25 in the numerator, and 1 in the denominator to cross off units:

\[

{Tab}~=~\frac{1~tab}{6.25~mg}~x~\frac{25~mg}{1}

\]

4. Cross out mg diagonally:

\[

{Tab}~=~\frac{1~tab}{6.25~\cancel{mg}}~x~\frac{25~\cancel{mg}}

\]

5. Multiply across the numerators and denominators, and then divide the final fraction to solve the problem:

\[

{Tab}~=~\frac{1~tab}{6.25~\cancel{mg}}~x~\frac{25~\cancel{mg}}{1}~=~{4~tabs}

\]