Week 4 Assignment – Calculation Applications

Career Relevancy
Although you may not realize it, translating and converting numbers are important parts of pharmacology. This might mean converting units of measurements from grams or maybe ounces to milligrams. In these types of everyday scenarios, you’ll need the skill sets to make connections and conversions on the fly. For instance, prescriptions usually require a specific measurement of medication dosage, but you may not always be provided this information in the same numerical system. To prevent errors in administering drugs to your patients, you’ll need to understand the fundamentals of the metric system—a core numerical framework in the medical system.


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Monique is almost finished building her orientation training for her hospital: Introduction to Pharmacology. It’s been an eye-opening experience, allowing her the unique opportunity to retrace her professional and educational steps. She’s been able to reflect on her knowledge of drug properties and functions and fill in the gaps in her understanding of policy and protocols. She’s also revisited some of the basic mathematical formulas that have become second nature to her, giving her the chance to consider how she learned about these calculations in the first place and how she can teach her colleagues about these core qualitative concepts.

Monique knows that nurses must be able to accurately convert medication dosages among three different measurement systems: apothecary, household, and metric. She had also discovered the importance of knowing basic calculation formulas so she wouldn’t need to rely on a calculator. She was still working on mastering those formulas and memorizing all the components of the metric system, but she was confident that she’d become familiar with them over time. Right now, though, one of her instructors was emphasizing the value of ratios and fractions in helping nurses accurately calculate formulas. Monique adds speaking notes to ensure she covers the following material:


There are times when the nurse may need to reconstitute medications or substances that patients need to consume. Instructions for reconstitution may require the nurse to use a ratio. In other cases, a medication may be ordered with a total amount given in divided doses in fractions. An example of this might be 100 mg qd of a liquid medication given over 4 doses. This is a simple division, and the nurse would explain to the patient that they should take 25 mg four times a day.

Another example of fractions could be an elixir that contains 100 mg of a certain medication in 250 ml of liquid, but the doctor has ordered 20 mg. This would require using a ratio or a fraction to calculate the amount of the liquid that would need to be given. Some injectable medications come to the hospital in a vial in powdered form, and the nurse injects the appropriate amount of normal saline or sterile water into the vial to reconstitute the medication. This requires a calculation, and unless the patient is to receive all the medication in the vial, yet another calculation using a ratio or fraction must be performed. Too much or too little medication can be life-threatening, so the nurse must be able to accurately perform mathematical functions using ratios and fractions. Whole numbers and decimals may be used to express some formulas; however, fractions and ratios are required for others.

Ratios are another way to express fractions. A ratio is a comparison of size or quantity. Ratios explain the relationship of the first number to the second. For instance, if you are diluting a vial of 50 mg penicillin with 100 ml normal saline, you would use a ratio to determine how many milligrams are in each milliliter. Each 1 ml of the solution now contains 0.5 mg penicillin.

As a nurse, you may also be the unit manager. If this is the case, you would need to calculate staffing ratios and determine whether additional people are needed. Ratios can help you with that. Let’s say you’re working as the office manager in an office with one physician who works 30 hours a week. At 40 hours a week, someone who works 30 hours would be considered ¾ time. You would need 4 people working full time to support this physician, but what if this doctor decides to work 40 hours? How many additional staff members do you need? You might calculate and express your staffing needs as a ratio. You divide the number of people in the office by the number of physicians in the office. Right now, you have 4 people to ¾ physician, expressed as 4 to 0.75 or 4:0.75. If the doctor increases their time to 40 hours per week, the office will need 5.33 FTEs, or full-time equivalents to run the office smoothly.

Ratios can also be used to express the dosage of medications and the amount of nutritional supplements for tube feedings. A doctor might order 0.5 mg/kg body weight in four divided doses. This would require that you first convert the patient’s weight from pounds to kilograms. If the patient weighs 67 kilograms, then you would multiply 67 times 0.5. The patient should receive 33.5 mg or 8.375 mg. four times a day. Ratios have many different uses in the hospital, and each of you as a nurse needs to be comfortable using them.

Using ratios require basic mathematical skills, and practice is the best way to ensure that you are comfortable with these calculations.

To convert a number of grams, g, to a number of milligrams, mg, we need to know the conversion factor, which is that there are 1000 mg in 1 g. If we want to know the number of mg in 5 g, we set up a ratio equation: 1000 mg: 1 g = x: 5 g, where x is the number of mg in 5 g. We now restate it as a fractional equation:Proportion of 5 g to mg

Then cross multiply to get rid of the fractional equation:

1000 mg * 5 g = x * 1 g

Then divide both sides by g and multiply the 1000 mg by 5:

5000 mg = x

So, we have calculated that 5 grams is equal to 5000 mg.

We can do the same between measurement systems as well. Suppose we find that, as a result of filling a prescription, that a 10 mL dose of amoxicillin is to be administered three times a day to an infant. We know that infants are dosed not in mL but in teaspoons. We have to convert 10 mL to a number of teaspoons.

Since we know that one teaspoonful is equal to 5 mL of liquid, we can set up the ratio equation as 5 mL: teaspoon = 10 mL: x and restate as a fractional equation:

proportion ml to tsp

Cross multiplying gives us:

5 mL * x = 10 mL * 1 tsp

Dividing each side by 5 mL gives us the answer:

x = 2 tsp

Monique knows that helping her others learn valuable skills will also help her have a successful career.

Resources and References

County of Los Angeles Public Health Nursing. (n.d.). Medication calculation examination study guide. Retrieved from http://publichealth.lacounty.gov/phn/docs/MCE%20Study%20Guiderevised6-10.pdf (Links to an external site.)

Power-Pak C.E. (n.d.). Pharmacy calculations for pharmacy technicians: Concentrations, dilutions and drug dosing. Retrieved from https://www.powerpak.com/course/print/115571 (Links to an external site.)

Thompson Health. (n.d.). Thompson health medication study guide for nursing candidates. Retrieved from https://www.thompsonhealth.com/Portals/0/_Careers/PDF/MedicationStudyGuide_Nov2011.pdf (Links to an external site.)

Making conversions and performing basic calculations are core elements of the medical practice. As a nurse, you’ll need to feel comfortable working through some of these mathematical equations.

For this assignment, you’re going to complete this worksheetPreview the document, which provides some conversion problems and calculations for you to solve.

Save your file as PHR101_Week4_Worksh

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