Problem 14 - Calculate With Confidence

Question

Calculate the dosages for the problems that follow, and indicate the number of milliliters you will administer. Shade in the dosage on the syringe provided. Use medication labels or information provided to calculate the volume necessary to administer the dosage ordered. Express your answers to the nearest tenth except where indicated. Order: Stadol \(1.5 \mathrm{mg}\) IM q4h p.r.n. for pain. Available: Stadol labeled \(2 \mathrm{mg}\) per \(\mathrm{mL}\)

Step-by-Step Solution

Answer

Administer 0.8 mL of Stadol.

Step 1: Understand the Given Information

We need to administer Stadol at a dosage of 1.5 mg intramuscularly (IM) for pain, whenever necessary. The available Stadol solution is labeled as containing 2 mg per mL.

Step 2: Set Up the Proportion for Dosage Calculation

We need to find out how much of the 2 mg/mL solution is needed to deliver a dose of 1.5 mg. We set up the proportion:\[\frac{1.5 \text{ mg}}{x \text{ mL}} = \frac{2 \text{ mg}}{1 \text{ mL}}\] where \(x\) is the volume in mL we need to find.

Step 3: Solve the Proportion

Cross-multiply to solve the equation: \(1.5 \times 1 = 2 \times x\), which simplifies to \(1.5 = 2x\). Divide both sides by 2 to isolate \(x\):\[x = \frac{1.5}{2} = 0.75 \text{ mL}\]

Step 4: Round to the Nearest Tenth

We need to round 0.75 mL to the nearest tenth as instructed. 0.75 rounded to the nearest tenth is 0.8 mL. Therefore, the required volume to administer is 0.8 mL.

Key Concepts

Medication Administration

When it comes to medication administration, precision and safety are key. Administering medication involves accurately giving the correct drug dosage to the patient, based on medical orders. It is essential because it affects treatment efficacy and patient well-being.

Healthcare professionals, like nurses and doctors, use medical orders to determine the correct medication, dosage, route (such as intramuscular or oral), and frequency. In the exercise, the route specified was intramuscular (IM), which requires particular care to avoid complications. Correct medication administration ensures therapeutic effectiveness and reduces the risk of side effects.

• Always confirm the patient's details and the medication order twice to prevent errors.
• Understand the purpose of the medication to efficiently monitor its effects.
• Use proper sterilization techniques to prevent infection during administration.

Understanding and performing correct medication administration ensures that patients receive the most benefit from their treatment.

Proportion Method

The proportion method is a fundamental math technique used in dosage calculations. It involves creating a mathematical equation where two ratios are set equal, allowing for easy solving of unknown values. This method is particularly useful in pharmacy and healthcare when calculating medication dosages.

In our example, we needed to find how much of a medication labeled at 2 mg/mL is needed to administer 1.5 mg dosage. We set up the proportion:\[\frac{1.5 \text{ mg}}{x \text{ mL}} = \frac{2 \text{ mg}}{1 \text{ mL}}\]Where \(x\) represents the required volume in mL.

To solve:

• Cross-multiply: \(1.5 \times 1 = 2 \times x\)
• Simplify to find \(x\), which means dividing both sides by 2 to isolate \(x\).

This method efficiently determines the required dosage volume with clear and straightforward steps.

Rounding Numbers

Rounding numbers is an important mathematical process that simplifies figures while maintaining a reasonable level of precision. In medication dosing, rounding is often used to ensure amounts can be practically measured and administered.

In the solution, we ended up with 0.75 mL, but the instructions asked for the dosage to be rounded to the nearest tenth. Rounding involves examining the number in the hundredths place and adjusting the tenths place accordingly. If the hundredths digit is 5 or more, increase the tenths digit by one.

• 0.75 rounds to 0.8 when rounding to the nearest tenth.
• This step ensures accuracy without unnecessary complexity.

Rounding helps maintain clarity and practicality in administering medication and avoids confusion in communication among healthcare providers.