Question

A prescription medication requires \(7.55 \mathrm{mg}\) per \(\mathrm{kg}\) of body weight. Convert this quantity to the number of grams required per pound of body weight and determine the correct dose (in \(g\) ) for a 175-lb patient.

Short answer

The correct dose for a 175-lb patient is 0.5992 grams.

Step-by-step solution

Convert milligrams to grams

As there are 1000 milligrams (mg) in a gram (g), divide 7.55 mg by 1000 to convert the dosage to grams per kilogram of body weight.

Calculate dosage in grams per kilogram

Perform the division: \[ 7.55 \, \text{mg} \times \frac{1 \, \text{g}}{1000 \, \text{mg}} = 0.00755 \, \text{g} \]

Convert kilograms to pounds

There are approximately 2.20462 pounds in a kilogram. To find the number of grams required per pound, divide the dosage in grams per kilogram by 2.20462.

Calculate dosage in grams per pound

Perform the division: \[ 0.00755 \, \text{g/kg} \div 2.20462 \, \text{lb/kg} = 0.003424 \, \text{g/lb} \]

Determine dose for a 175-lb patient

Multiply the dosage in grams per pound by the patient's weight in pounds to find the correct dose in grams for the patient. \[ 0.003424 \, \text{g/lb} \times 175 \, \text{lb} = 0.5992 \, \text{g} \]

Key concepts

Unit Conversion

Unit conversion is a critical process in various fields, including medicine, where precise measurements can be pivotal to treatment outcomes. In the context of medical dosages, it is essential to accurately convert units from one system to another to ensure patients receive the correct amount of medication. For instance, in the given exercise, we convert a medication dosage from milligrams (mg) per kilogram (kg) to grams (g) per pound (lb). This involves two main steps: converting milligrams to grams, and then converting kilograms to pounds. Since there are 1000 milligrams in one gram, and approximately 2.20462 pounds in one kilogram, these conversion factors are used to recalibrate the dosage to the appropriate unit for the patient's weight in pounds. Understanding these basic units and how to convert between them is essential, as it allows for seamless adjustments in dosing to accommodate different measurement systems used globally.

Medical Dosage

Accurately calculating medical dosages is of utmost importance for patient safety and efficacy of treatment. A medical dosage refers to the frequency, quantity, and number of doses to be administered to a patient. It's often determined based on various factors, including the patient's age, weight, and the nature of the illness. In our example, the dosage of 7.55 mg per kg body weight must be translated into a real-world measure that's applicable to the patient, requiring an understanding of dosage calculation as well as unit conversion. Through step-by-step calculations, we ensure that a dosage is not only correct but also meaningful in a practical setting, avoiding potential underdosing or overdosing. Proper calculation assures that the medicine administered will perform as intended without unwarranted side effects.

Metric System

The metric system is an international system of measurement that is used widely in the field of healthcare. Its units for mass are grams (g) and kilograms (kg), which are crucial in medical dosage calculations. When healthcare providers communicate dosages and instructions, they often use the metric system due to its universal acceptance and ease of conversion between units. This system's reliance on multiples of ten simplifies the process of scaling dosages up or down, as seen when converting milligrams to grams in our exercise. Familiarity with the metric system allows healthcare professionals and patients alike to interact with dosages in a clear and consistent manner, reducing the risk of errors in medication administration.

Weight-Based Medication Dosing

Weight-based medication dosing is a precise method used to personalize medicine administration based on the weight of the patient. This is particularly important for certain drugs where the same dose may not be suitable for all individuals. For example, a substance that is safe and effective at a particular concentration in a heavier individual may be too strong and unsafe for someone lighter. In the exercise's context, the patient's weight is taken into account to calculate the exact dosage of medication needed, which is determined to be 0.5992 grams for a 175-lb patient. It highlights the importance of accurate weight measurements and careful arithmetic to calculate and administer a dose that is safe while therapeutically effective for patients of varying sizes.