Question

Calculate the volume necessary (in milliliters) to provide the dosage ordered, using medication labels where available. Express your answer as a decimal fraction to the nearest tenth where indicated. Order: Gentamicin \(90 \mathrm{mg}\) IV \(\mathrm{q} 8 \mathrm{~h}\). Available: Gentamicin \(40 \mathrm{mg}\) per \(\mathrm{mL}\) _______.

Short answer

2.3 mL is needed for the 90 mg dose.

Step-by-step solution

Understand the Problem

We need to determine how many milliliters of a 40 mg/mL Gentamicin solution are required to administer a dose of 90 mg. The available concentration is 40 mg of Gentamicin per milliliter.

Set Up Ratio Equation

The medication concentration can be expressed as a ratio:\[ \frac{40 \text{ mg}}{1 \text{ mL}} \]We need to find how many milliliters contain 90 mg. Let's set up the equation:\[ \frac{40 \text{ mg}}{1 \text{ mL}} = \frac{90 \text{ mg}}{x \text{ mL}} \]

Solve for x

To find the value of \(x\), which represents the number of milliliters needed, cross-multiply:\[ 40x = 90 \times 1 \]Simplifying this gives:\[ 40x = 90 \]Next, solve for \(x\) by dividing both sides by 40:\[ x = \frac{90}{40} \]

Perform the Calculation

Divide 90 by 40 to solve for \(x\): \[ x = 2.25 \]

Round to the Nearest Tenth

We need to express the answer as a decimal fraction to the nearest tenth. The calculation yields 2.25, which rounds to 2.3 since the hundredth place (5) rounds the tenth place up.

Key concepts

Dosage Calculation

Dosage calculation is an essential skill for healthcare professionals to ensure patient safety and the effectiveness of medication regimens. It involves determining the amount of medication a patient needs to achieve the therapeutic effect without causing harm. In our example, we need a dose of 90 mg of Gentamicin. Calculating the correct dosage involves taking into account the concentration of the medication available. Healthcare professionals must be familiar with equations and proportion methods to perform these tasks accurately.

It often requires basic math operations, such as division and multiplication, and sometimes knowledge of conversions between units if they differ from the desired outcome.

Always make sure to double-check calculations to avoid mistakes that could affect patient care.

• Identify the dose ordered and the concentration available.
• Use simple arithmetic operations to calculate the required dosage.
• Verify calculations by considering patient-specific factors.

IV Medication Administration

With intravenous (IV) medication administration, drugs are delivered directly into the bloodstream, allowing for quick therapeutic effects. This route of administration is often used when a rapid onset of action is required or for medications that cannot be effectively given orally.

An important consideration in IV medication administration is the exact dosage and fluid volume to ensure patient safety and efficacy. In our example, we calculate the volume necessary to administer Gentamicin intravenously, ensuring that the patient receives precisely the prescribed amount.

• Ensure correct IV dosage to avoid under-dosing or overdosing.
• Double-check patient identification for safety.
• Monitor patients for adverse reactions during and after administration.

Proper technique and careful calculation ensure that the medication is effective, reducing potential risks associated with IV therapy.

Ratio and Proportion

The method of ratio and proportion is a mathematical approach used extensively in medication calculations. It involves expressing two quantities as a fraction and setting this equal to another fraction - a proportion. This allows for solving for an unknown quantity that is part of the proportion.

In our step-by-step solution, we set up a ratio with the equation \( \frac{40 \text{ mg}}{1 \text{ mL}} = \frac{90 \text{ mg}}{x \text{ mL}} \). This equation illustrates the proportion between the available concentration and the desired dose. To find the unknown \(x\), representing the volume in milliliters, we cross-multiply and solve for the unknown.

• Set up the ratio based on available data.
• Cross-multiply to simplify and solve the equation.
• Divide to isolate the unknown variable and find your answer.

Mastery of ratio and proportion is crucial in healthcare to ensure accurate medication delivery.

Volume Calculation in Milliliters

Volume calculation in milliliters is a frequent task in healthcare settings, especially for liquid medication dosages. This practice is particularly important in IV administrations where precision can impact treatment outcomes significantly.

In our example, we calculated the volume of Gentamicin needed by determining how many milliliters were required to meet the 90 mg dose using a 40 mg/mL concentration. The resulting calculation was 2.25 mL, which is then rounded to the nearest tenth, giving us 2.3 mL.

• Use the concentration information to determine needed volume.
• Perform accurate calculations to achieve the prescribed dosage.
• Round calculations appropriately based on specific guidelines (e.g., nearest tenth).

An accurate volume calculation ensures that patients receive their medications safely and effectively, aligning with healthcare best practices.