Question

A prescription medication requires \(0.00225\) g per lb of body weight. Convert this quantity to the number of mg required per kg of body weight and determine the correct dose (in \(\mathrm{mg}\) ) for a \(105-\mathrm{kg}\) patient.

Short answer

The correct dose for a 105-kg patient is 107.25 mg.

Step-by-step solution

Convert grams to milligrams

Knowing that there are 1000 milligrams (mg) in a gram (g), convert the prescribed dose from grams to milligrams by multiplying by 1000.

Convert pounds to kilograms

There are approximately 2.20462 pounds (lb) in one kilogram (kg). To find the dose per kg, divide the dose in mg per lb by 2.20462.

Calculate the dose for the patient

Now that we have the dose in mg per kg, multiply this by the patient's weight in kg to find the correct dose.

Key concepts

Unit Conversion

Understanding unit conversion is crucial when dealing with medication dosages, as it ensures that patients receive the correct amount of medication based on their weight, which could be measured in a different system of units. In the example provided, the prescription requires an initial step of converting the medication dosage from grams to milligrams.

Since 1 gram equals 1000 milligrams, to convert from grams to milligrams, you multiply the dose by 1000. This straightforward multiplication is the foundation for unit conversion in pharmaceutical applications. It's essential to be familiar with common conversions, such as 1 kg equaling 2.20462 pounds, to switch seamlessly between the metric system (used predominantly in medical settings) and the Imperial or US customary units. These conversions ensure accuracy and safety in medication administration.

Medication Dosage

For medication dosages, determining the correct amount of a drug to administer based on the patient's body weight is a fundamental principle in pharmaceutical practices. As weight can directly influence how a person responds to a medication, dosages are often prescribed in mass (such as grams or milligrams) per unit of body weight (like pounds or kilograms).

The exercise's step-by-step solution indicates the need to first convert the medication dosage from grams to milligrams, then adjust this dosage according to the patient's weight by converting pounds to kilograms. This two-step process underlines the patient-centric approach in pharmaceutical mathematics, which aims to tailor the dosage to each individual's specific needs, reducing the risk of underdosing or overdosing, which could lead to ineffective treatment or adverse effects, respectively.

Pharmaceutical Mathematics

Pharmaceutical mathematics encompasses a variety of calculations that are vital for the safe administration of medication. It incorporates concepts from arithmetic, algebra, and sometimes even calculus, to solve problems related to drug dosages, infusion rates, and medication conversions. In this example, the steps include conversions of weight and mass, followed by multiplication to factor in the patient's actual weight.

To ensure safety and efficacy, pharmacists and healthcare professionals must use precise calculations. This can mean converting between different units of mass and volume, adjusting dosages based on patient-specific factors, and calculating appropriate infusion times. Math skills are thus an indispensable part of pharmaceutical training, as errors in computation can lead to serious consequences for patient health.