Question

Calculate the dosages to be given. Round answers to the nearest tenth as indicated (express answers in milliliters). Order: Tylenol 0.4 g p.o. q4h p.r.n. for temp greater than \(101^{\circ} \mathrm{F}\). Available: Tylenol elixir labeled \(160 \mathrm{mg}\) per \(5 \mathrm{~mL}\)

Short answer

The dosage to be given is 12.5 mL.

Step-by-step solution

Convert Order from Grams to Milligrams

The order is for 0.4 grams of Tylenol. To convert grams to milligrams, multiply by 1000. Therefore, \(0.4 \text{ g} = 400 \text{ mg}\).

Identify the Concentration

The available Tylenol elixir is labeled with a concentration of 160 mg per 5 mL. This means for every 5 mL of elixir, there are 160 mg of Tylenol.

Set Up the Proportion

Set up a proportion to solve for the volume (\(x\) mL) needed to provide 400 mg of Tylenol: \( \frac{160 \text{ mg}}{5 \text{ mL}} = \frac{400 \text{ mg}}{x \text{ mL}} \).

Solve for x

Cross-multiply to solve for \(x\). This gives: \(160x = 2000\). Divide both sides by 160 to find \(x = \frac{2000}{160} = 12.5 \text{ mL}\).

Round to the Nearest Tenth

The calculated dosage is 12.5 mL, which is already rounded to the nearest tenth.

Key concepts

Unit Conversion

When dealing with medication dosages, understanding unit conversion is crucial. In this exercise, the initial order for Tylenol is given in grams, but the solution requires milligrams since the Tylenol elixir's concentration is listed in this unit. To convert grams to milligrams, you simply multiply the number of grams by 1000.
For instance, 0.4 grams of Tylenol is equivalent to 0.4 multiplied by 1000, resulting in 400 milligrams.
This conversion ensures that all measurements are in the same unit, making subsequent calculations straightforward. Converting units accurately is vital to avoid potential dosing errors and to ensure patient safety.

Proportion Method

The proportion method is a powerful tool for finding the unknown value in problems involving ratios or concentrations.
In this scenario, you are tasked with determining how many milliliters of elixir are needed to provide 400 mg of Tylenol.
Since you know that 160 mg of Tylenol is contained in 5 mL of the elixir, you can set up the proportion as follows: \( \frac{160 \text{ mg}}{5 \text{ mL}} = \frac{400 \text{ mg}}{x \text{ mL}} \). By cross-multiplying, you can solve for \(x\), the unknown quantity of liquid needed. This gives you the equation: \(160x = 2000\). Finally, dividing both sides by 160 results in \(x = 12.5 \text{ mL}\). The proportion method is efficient and reduces errors in pharmaceutical calculations.

Rounding Numbers

Rounding numbers is a common practice in medication dosage calculations to ensure precision and practicality in administering doses.
In this instance, the dosage calculated is 12.5 mL.
Since the instruction specifies rounding to the nearest tenth, this value is already appropriately rounded.
Rounding is essential as some measurement tools, like syringes or dispensing cups, may not accurately measure very fine units. Additionally, rounding to a standard measurement unit makes it easier for healthcare providers to administer the dosage without confusion or error.

Pharmaceutical Calculations

Pharmaceutical calculations combine several mathematical skills and are integral for determining correct medication dosages.
This exercise encompasses unit conversion, use of proportions, and rounding, all of which are fundamental components of pharmaceutical math.
Accurate calculations ensure the correct dosage, which is vital for the safety and efficacy of the medication. Moreover, developing proficiency in pharmaceutical calculations is important for healthcare professionals to maintain patient trust and ensure optimal therapeutic outcomes. These calculations are a part of daily practice and must be performed meticulously to provide the highest standard of care.