Dimensional Analysis
Calculating Dosages Safely
3rd Edition
• Author(s)Tracy Horntvedt
TEST BANK
1)
Reference
Ch. 1 — Whole Numbers — Types of Numbers / Division
Clinical stem
The provider orders: Give glycopyrrolate 200 mcg IV once. On
the medication cart is glycopyrrolate 0.2 mg/mL ampules. Using
dimensional analysis, calculate the volume to draw up in mL.
(Use whole-number arithmetic; express final answer as a whole
number or whole-number mL when appropriate.)
A. 1 mL
B. 0.5 mL
,C. 2 mL
D. 0.2 mL
Correct answer: A. 1 mL
Rationales
Correct (A): Setup: ordered 200 mcg × (0.2 mg / 1 mL) but must
convert mcg → mg: 200 mcg × (1 mg / 1000 mcg) = 0.2 mg.
Dimensional analysis: 0.2 mg × (1 mL / 0.2 mg) = 1 mL. Units
cancel correctly to mL. Whole-number arithmetic used (0.2 mg
equals 200 mcg) and result is a practical whole mL to draw up;
rounding not needed. Clinically safe and matches supply
concentration.
B (0.5 mL): Error: Likely halved the conversion (inverted ratio) or
divided mg by 2. Shows inversion of the concentration ratio.
Unsafe because underdoses.
C (2 mL): Error: Moved decimal right one place (×10) —
common decimal misplacement. Would overdose the patient.
D (0.2 mL): Error: Mistook 200 mcg as 0.02 mg (decimal error)
or used wrong conversion factor (1 mg = 10,000 mcg).
Underdose risk.
Teaching point: Always convert mcg ↔ mg before dimensional
setup; track decimal placement carefully.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
2)
,Reference
Ch. 1 — Whole Numbers — Multiplying Whole Numbers
Clinical stem
Provider orders: Give amoxicillin 500 mg PO every 8 hours for 7
days. The dispenser provides 250 mg tablets. Using dimensional
analysis, calculate the total number of tablets the nurse should
dispense for the full course (whole number required).
A. 21 tablets
B. 42 tablets
C. 14 tablets
D. 28 tablets
Correct answer: B. 42 tablets
Rationales
Correct (B): Per dose: 500 mg ÷ 250 mg/tablet = 2 tablets per
dose. Doses per day: 24 ÷ 8 = 3 doses/day. Total tablets: 2
tablets/dose × 3 doses/day × 7 days = 42 tablets. Multiplication
of whole numbers yields whole-tablet count. Clinically
appropriate to dispense whole tablets.
A (21): Error: Forgot to multiply by 2 tablets/dose (only counted
one tablet per dose). Common omission of a multiplication
step. Underdoses patient.
C (14): Error: Calculated 2 tablets/day × 7 days (confused
doses/day with tablets/day). Reflects mixing of units.
D (28): Error: Used 4 doses/day (6-hour schedule) instead of 3;
common mistake converting hours to doses. Would
overdispense.
, Teaching point: Convert ordered dose to tablets first, then
multiply by doses/day × days.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
3)
Reference
Ch. 1 — Whole Numbers — Subtracting Whole Numbers
Clinical stem
A PRN order reads: Morphine 2 mg IV q2h PRN pain, max 12 mg
in 24 hours. The patient has already received 6 mg in the past
12 hours. Using dimensional analysis, how many additional
whole 2 mg doses can be given in the remaining 24-hour period
without exceeding the maximum?
A. 3 doses
B. 6 doses
C. 2 doses
D. 4 doses
Correct answer: A. 3 doses
Rationales
Correct (A): Max allowable remaining: 12 mg − 6 mg = 6 mg
remaining. Number of 2 mg doses remaining: 6 mg ÷ 2 mg/dose
= 3 doses. Subtraction then division of whole numbers gives
whole-dose count. Clinically ensures max is not exceeded.
B (6): Error: Misread remaining mg as 12 mg and divided by 2
Calculating Dosages Safely
3rd Edition
• Author(s)Tracy Horntvedt
TEST BANK
1)
Reference
Ch. 1 — Whole Numbers — Types of Numbers / Division
Clinical stem
The provider orders: Give glycopyrrolate 200 mcg IV once. On
the medication cart is glycopyrrolate 0.2 mg/mL ampules. Using
dimensional analysis, calculate the volume to draw up in mL.
(Use whole-number arithmetic; express final answer as a whole
number or whole-number mL when appropriate.)
A. 1 mL
B. 0.5 mL
,C. 2 mL
D. 0.2 mL
Correct answer: A. 1 mL
Rationales
Correct (A): Setup: ordered 200 mcg × (0.2 mg / 1 mL) but must
convert mcg → mg: 200 mcg × (1 mg / 1000 mcg) = 0.2 mg.
Dimensional analysis: 0.2 mg × (1 mL / 0.2 mg) = 1 mL. Units
cancel correctly to mL. Whole-number arithmetic used (0.2 mg
equals 200 mcg) and result is a practical whole mL to draw up;
rounding not needed. Clinically safe and matches supply
concentration.
B (0.5 mL): Error: Likely halved the conversion (inverted ratio) or
divided mg by 2. Shows inversion of the concentration ratio.
Unsafe because underdoses.
C (2 mL): Error: Moved decimal right one place (×10) —
common decimal misplacement. Would overdose the patient.
D (0.2 mL): Error: Mistook 200 mcg as 0.02 mg (decimal error)
or used wrong conversion factor (1 mg = 10,000 mcg).
Underdose risk.
Teaching point: Always convert mcg ↔ mg before dimensional
setup; track decimal placement carefully.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
2)
,Reference
Ch. 1 — Whole Numbers — Multiplying Whole Numbers
Clinical stem
Provider orders: Give amoxicillin 500 mg PO every 8 hours for 7
days. The dispenser provides 250 mg tablets. Using dimensional
analysis, calculate the total number of tablets the nurse should
dispense for the full course (whole number required).
A. 21 tablets
B. 42 tablets
C. 14 tablets
D. 28 tablets
Correct answer: B. 42 tablets
Rationales
Correct (B): Per dose: 500 mg ÷ 250 mg/tablet = 2 tablets per
dose. Doses per day: 24 ÷ 8 = 3 doses/day. Total tablets: 2
tablets/dose × 3 doses/day × 7 days = 42 tablets. Multiplication
of whole numbers yields whole-tablet count. Clinically
appropriate to dispense whole tablets.
A (21): Error: Forgot to multiply by 2 tablets/dose (only counted
one tablet per dose). Common omission of a multiplication
step. Underdoses patient.
C (14): Error: Calculated 2 tablets/day × 7 days (confused
doses/day with tablets/day). Reflects mixing of units.
D (28): Error: Used 4 doses/day (6-hour schedule) instead of 3;
common mistake converting hours to doses. Would
overdispense.
, Teaching point: Convert ordered dose to tablets first, then
multiply by doses/day × days.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
3)
Reference
Ch. 1 — Whole Numbers — Subtracting Whole Numbers
Clinical stem
A PRN order reads: Morphine 2 mg IV q2h PRN pain, max 12 mg
in 24 hours. The patient has already received 6 mg in the past
12 hours. Using dimensional analysis, how many additional
whole 2 mg doses can be given in the remaining 24-hour period
without exceeding the maximum?
A. 3 doses
B. 6 doses
C. 2 doses
D. 4 doses
Correct answer: A. 3 doses
Rationales
Correct (A): Max allowable remaining: 12 mg − 6 mg = 6 mg
remaining. Number of 2 mg doses remaining: 6 mg ÷ 2 mg/dose
= 3 doses. Subtraction then division of whole numbers gives
whole-dose count. Clinically ensures max is not exceeded.
B (6): Error: Misread remaining mg as 12 mg and divided by 2
