HS140 Unit 3 Dosage Calculation Practice Set Example

Every Unit at Every Step: A Unit 3 Dosage Calculation Set Worked by Dimensional Analysis

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Purdue University Global

HS140: Pharmacology

Unit 3 Dosage Calculation Set

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[Date]

All figures are invented practice problems, not dosing guidance; the safety source cited is real.

Method

Each problem uses dimensional analysis: the starting quantity is multiplied by conversion factors arranged so that unwanted units cancel, leaving the unit the question asks for. Every line shows the units. Answers follow the rounding rule given in each problem. Leading zeros are always written and trailing zeros never, as medication safety lists require (Institute for Safe Medication Practices, 2021).

Problems

Problem 1. Convert 0.25 mg to micrograms. 0.25 mg x 1,000 mcg / 1 mg = 250 mcg. The milligram units cancel, leaving micrograms. Check: a microgram is smaller, so the number should get larger, and it did.

Problem 2. A child weighs 44 lb. What is the weight in kilograms? 44 lb x 1 kg / 2.2 lb = 20 kg. Check: kilograms are heavier units, so the number should be smaller, and it is.

Problem 3. An order reads 15 mg/kg for the 20 kg child. How many milligrams is one dose? 20 kg x 15 mg / 1 kg = 300 mg.

Problem 4. Tablets are 150 mg each. How many tablets provide 300 mg? 300 mg x 1 tablet / 150 mg = 2 tablets.

Problem 5. A liquid contains 160 mg in 5 mL. How many milliliters provide 300 mg? Round to the nearest tenth. 300 mg x 5 mL / 160 mg = 1,500 / 160 = 9.375 mL, rounded to 9.4 mL. Check: 160 mg is in 5 mL, so 300 mg should need a little less than twice 5 mL, and 9.4 mL fits.

Problem 6. An adult weighing 154 lb is ordered 0.5 mg/kg. Find the dose in milligrams. 154 lb x 1 kg / 2.2 lb = 70 kg. 70 kg x 0.5 mg / 1 kg = 35 mg.

Problem 7. A vial contains 2 mg/mL. How many milliliters deliver 35 mg? 35 mg x 1 mL / 2 mg = 17.5 mL.

Problem 8. A pump must deliver 900 mL over 6 hours. What rate should be set, in mL per hour? 900 mL / 6 h = 150 mL/h. Units: mL over h leaves mL/h, the unit pumps use.

Writing the unit at every step is what catches a wrong conversion before it becomes a wrong dose, because a calculation that ends in the wrong unit announces its own error.

Common Errors and How the Method Prevents Them

Three errors are common in practice problems. The first is dividing by 2.2 when converting kilograms to pounds, or multiplying when converting pounds to kilograms; writing the units shows which way the factor must go. The second is a missing leading zero, so that 0.5 mg is read as 5 mg, a tenfold error; the set writes 0.5 in every case. The third is confusing milligrams and micrograms, a thousandfold error; problem 1 shows the conversion explicitly.

Reasonableness Checks

After each answer, a quick check asked whether the size of the number made sense: larger when converting to a smaller unit, about twice as large when the dose doubled. In problem 5, the check confirmed that 9.4 mL is just under two 5 mL portions. These checks take seconds and catch errors that arithmetic alone can miss (Lilley et al., 2023).

Weight-based dosing appears often in pediatrics because children's drug handling scales with size (Katzung & Vanderah, 2021), which is why problems 2 and 3 convert weight before calculating the dose.

Limits

The problems practice arithmetic and unit handling with invented figures. Real dosing depends on the prescriber's order, the facility's policies and verified drug references.

References

Institute for Safe Medication Practices. (2021). ISMP list of error-prone abbreviations, symbols, and dose designations. Institute for Safe Medication Practices.

Katzung, B. G., & Vanderah, T. W. (Eds.). (2021). Basic and clinical pharmacology (15th ed.). McGraw Hill.

Lilley, L. L., Collins, S. R., & Snyder, J. S. (2023). Pharmacology and the nursing process (10th ed.). Elsevier.