Question

Using conversion factors, solve each of the following clinical problems: a. The physician has ordered \(1.0 \mathrm{~g}\) of tetracycline to be given every 6 hours to a patient. If your stock on hand is 500 -mg tablets, how many will you need for 1 day's treatment? b. An intramuscular medication is given at \(5.00 \mathrm{mg} / \mathrm{kg}\) of body weight. If you give \(425 \mathrm{mg}\) of medication to a patient, what is the patient's weight in pounds? c. A physician has ordered \(0.50 \mathrm{mg}\) of atropine, intramuscularly. If atropine were available as \(0.10 \mathrm{mg} / \mathrm{mL}\) of solution, how many milliliters would you need to give?

Short answer

8 tablets/day. 187.39 lbs. 5 mL.

Step-by-step solution

- Determine Required Tablets Per Dose

The physician ordered 1.0 g of tetracycline every 6 hours. Since each tablet contains 500 mg, convert 1.0 g to mg (1.0 g = 1000 mg). Divide the required dose by the tablet dosage: \ \[ \frac{1000 \text{ mg}}{500 \text{ mg/tablet}} = 2 \text{ tablets} \]

- Calculate Tablets Needed for 1 Day

The patient needs to take the medication every 6 hours, so there will be 4 doses in 1 day (24 hours / 6 hours per dose = 4 doses). Multiply the number of tablets per dose by the number of doses per day: \ \[ 2 \text{ tablets/dose} \times 4 \text{ doses/day} = 8 \text{ tablets/day} \]

- Identify Patient's Weight Using Conversion Factor

The medication dosage is given as 5.00 mg/kg body weight and the total medication given is 425 mg. Find the patient's weight in kg: \ \[ \frac{425 \text{ mg}}{5.00 \text{ mg/kg}} = 85 \text{ kg} \]

- Convert Patient's Weight to Pounds

Use the conversion factor 1 kg = 2.20462 lbs to find the weight in pounds: \ \[ 85 \text{ kg} \times 2.20462 \text{ lbs/kg} = 187.3927 \text{ lbs} \]

- Calculate Volume of Atropine Solution

The ordered dose is 0.50 mg of atropine and the concentration of the solution is 0.10 mg/mL. Determine the required volume: \ \[ \frac{0.50 \text{ mg}}{0.10 \text{ mg/mL}} = 5 \text{ mL} \]

Key concepts

conversion factors

Understanding conversion factors is essential in clinical calculations. A conversion factor is a ratio used to express a quantity in different units. For example, to convert grams to milligrams, we use the conversion factor of 1 gram = 1000 milligrams.
This concept is crucial in ensuring correct dosages, as medication orders often need to be converted to match the units available in the stock.
By using conversion factors, you simply multiply the quantity by the appropriate conversion ratio. This keeps the numerical relationship between quantities accurate.
For exercises like converting kg to pounds, remember that 1 kilogram equals 2.20462 pounds. This allows you to shift between units seamlessly, making sure you administer the right dose.

dosage calculations

Dosage calculations determine how much of a medication is needed for effective treatment. For instance, if a medication is prescribed in grams but available in milligrams, the dosage needs to be correctly calculated to ensure safe and accurate administration.
Let's break down an example: the physician orders 1.0 g of tetracycline every 6 hours. Since each tablet available is 500 mg, you need to convert grams to milligrams first. Using the conversion factor (1 g = 1000 mg), 1.0 g equals 1000 mg.
Divide the required dose (1000 mg) by the dosage per tablet (500 mg), resulting in 2 tablets per dose. If the medication is to be administered every 6 hours, or 4 times a day, the total number of tablets required per day is 2 tablets per dose times 4 doses, equaling 8 tablets.

medication administration

Effective medication administration involves understanding the dosage requirements and accurately measuring the medication to ensure patient safety. This process often entails converting measurements and calculating the correct dose.
For example, administering an intramuscular medication dosed at 5.00 mg/kg of body weight requires knowing the patient's weight. If a patient needs 425 mg of medication, you first find the weight in kilograms by dividing the total dose by the dose per kilogram: 425 mg divided by 5.00 mg/kg equals 85 kg.
Next, converting the patient's weight from kilograms to pounds using the conversion factor (1 kg = 2.20462 lbs) ensures you have the correct and easily understood patient weight in pounds.

unit conversions

Unit conversions are essential in clinical calculations to ensure the correct dosage is administered. Converting units may involve length, weight, volume, or concentration measurements.
In clinical settings, a common conversion involves converting between milligrams (mg) and milliliters (mL). For example, if a physician orders 0.50 mg of atropine and the solution available is 0.10 mg/mL, you need to determine the volume to administer.
Using the ratio (0.10 mg/mL), divide the required dose (0.50 mg) by the concentration (0.10 mg/mL), resulting in 5 mL of solution needed. Mastering unit conversions ensures appropriate medication administration and patient safety, making it a crucial skill for healthcare professionals.