Dimensional Analysis
Calculating Dosages Safely
3rd Edition
• Author(s)Tracy Horntvedt
TEST BANK
1
Reference: Ch. 1 — Whole Numbers — Dividing Whole
Numbers (tablet calculation)
Stem: A provider orders 1500 mg oral acetaminophen. At
bedside the nurse has 500 mg tablets. Using dimensional
analysis, how many whole tablets should the nurse administer?
(Assume tablets may not be split.)
A. 2 tablets
B. 3 tablets
C. 4 tablets
D. 1 tablet
,Correct answer: B. 3 tablets
Rationale — Correct: Setup: 1500 mg×1 tablet500 mg=31500\
\text{mg} \times \dfrac{1\ \text{tablet}}{500\ \text{mg}} =
31500 mg×500 mg1 tablet=3 tablets. Units cancel (mg→tablet).
The arithmetic is 1500÷500=31500\div500=31500÷500=3. This
is an exact whole number so no rounding needed; 3 tablets
meets the ordered dose safely.
Rationale — A: (2 tablets) reflects dividing incorrectly (1500 ÷
750 or halving the denominator) — underdosing.
Rationale — C: (4 tablets) reflects multiplying instead of
dividing or using 375 mg per tablet (math error) — results in
overdose.
Rationale — D: (1 tablet) shows decimal misplacement
(assuming 1500→1.5 and truncating) — underdose.
Teaching point: Always set up as (ordered amount) × (1 supply
unit / supply amount).
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
2
Reference: Ch. 1 — Whole Numbers — Division &
Multiplication (vial count)
Stem: A provider orders 250 mL of normal saline to be added
to a medication. Pharmacy sent 50 mL vials. How many whole
vials must the nurse prepare? (Vials cannot be partially used.)
,A. 3 vials
B. 4 vials
C. 5 vials
D. 6 vials
Correct answer: C. 5 vials
Rationale — Correct: Setup: 250 mL×1 vial50 mL=5250\
\text{mL} \times \dfrac{1\ \text{vial}}{50\ \text{mL}} =
5250 mL×50 mL1 vial=5 vials. Units cancel (mL→vial).
250÷50=5250\div50=5250÷50=5 whole vials; exact, no
rounding.
Rationale — A: (3) likely from incorrect subtraction
(250−50−50) or undercounting — underprepares.
Rationale — B: (4) likely from dividing by 60 or arithmetic
mistake (250 ÷ 60 ≈ 4.16) — incorrect divisor.
Rationale — D: (6) suggests overestimation or incorrect
multiplication (50×6=300 mL) — wasteful/incorrect.
Teaching point: Convert ordered volume to supply units; cancel
mL before counting vials.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
3
Reference: Ch. 1 — Whole Numbers — Multiplication &
Division (drop rate)
Stem: An IV infusion is set at 60 mL/hr using administration
, tubing with a 20 gtt/mL drop factor. Using dimensional analysis,
what is the correct delivery in gtt/min?
A. 10 gtt/min
B. 60 gtt/min
C. 20 gtt/min
D. 40 gtt/min
Correct answer: C. 20 gtt/min
Rationale — Correct: Setup:
60 mL/hr×1 hr60 min×20 gtt1 mL=20 gtt/min.60\
\text{mL/hr}\times\dfrac{1\ \text{hr}}{60\
\text{min}}\times\dfrac{20\ \text{gtt}}{1\ \text{mL}} = 20\
\text{gtt/min}.60 mL/hr×60 min1 hr×1 mL20 gtt=20 gtt/min.
Cancel hr and mL units. Compute: 60÷60=160\div60=160÷60=1
mL/min; 1×20=201\times20=201×20=20 gtt/min.
Rationale — A: (10) likely from halving the drop factor or
dividing by 120 instead of 60 — common arithmetic error.
Rationale — B: (60) reflects multiplying 60 mL/hr directly by 1
gtt/mL (forgetting drop factor) — unit error.
Rationale — D: (40) suggests using a 40 gtt/mL factor by
mistake — wrong tubing factor.
Teaching point: Always convert hours → minutes (÷60) before
applying gtt/mL.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
Calculating Dosages Safely
3rd Edition
• Author(s)Tracy Horntvedt
TEST BANK
1
Reference: Ch. 1 — Whole Numbers — Dividing Whole
Numbers (tablet calculation)
Stem: A provider orders 1500 mg oral acetaminophen. At
bedside the nurse has 500 mg tablets. Using dimensional
analysis, how many whole tablets should the nurse administer?
(Assume tablets may not be split.)
A. 2 tablets
B. 3 tablets
C. 4 tablets
D. 1 tablet
,Correct answer: B. 3 tablets
Rationale — Correct: Setup: 1500 mg×1 tablet500 mg=31500\
\text{mg} \times \dfrac{1\ \text{tablet}}{500\ \text{mg}} =
31500 mg×500 mg1 tablet=3 tablets. Units cancel (mg→tablet).
The arithmetic is 1500÷500=31500\div500=31500÷500=3. This
is an exact whole number so no rounding needed; 3 tablets
meets the ordered dose safely.
Rationale — A: (2 tablets) reflects dividing incorrectly (1500 ÷
750 or halving the denominator) — underdosing.
Rationale — C: (4 tablets) reflects multiplying instead of
dividing or using 375 mg per tablet (math error) — results in
overdose.
Rationale — D: (1 tablet) shows decimal misplacement
(assuming 1500→1.5 and truncating) — underdose.
Teaching point: Always set up as (ordered amount) × (1 supply
unit / supply amount).
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
2
Reference: Ch. 1 — Whole Numbers — Division &
Multiplication (vial count)
Stem: A provider orders 250 mL of normal saline to be added
to a medication. Pharmacy sent 50 mL vials. How many whole
vials must the nurse prepare? (Vials cannot be partially used.)
,A. 3 vials
B. 4 vials
C. 5 vials
D. 6 vials
Correct answer: C. 5 vials
Rationale — Correct: Setup: 250 mL×1 vial50 mL=5250\
\text{mL} \times \dfrac{1\ \text{vial}}{50\ \text{mL}} =
5250 mL×50 mL1 vial=5 vials. Units cancel (mL→vial).
250÷50=5250\div50=5250÷50=5 whole vials; exact, no
rounding.
Rationale — A: (3) likely from incorrect subtraction
(250−50−50) or undercounting — underprepares.
Rationale — B: (4) likely from dividing by 60 or arithmetic
mistake (250 ÷ 60 ≈ 4.16) — incorrect divisor.
Rationale — D: (6) suggests overestimation or incorrect
multiplication (50×6=300 mL) — wasteful/incorrect.
Teaching point: Convert ordered volume to supply units; cancel
mL before counting vials.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
3
Reference: Ch. 1 — Whole Numbers — Multiplication &
Division (drop rate)
Stem: An IV infusion is set at 60 mL/hr using administration
, tubing with a 20 gtt/mL drop factor. Using dimensional analysis,
what is the correct delivery in gtt/min?
A. 10 gtt/min
B. 60 gtt/min
C. 20 gtt/min
D. 40 gtt/min
Correct answer: C. 20 gtt/min
Rationale — Correct: Setup:
60 mL/hr×1 hr60 min×20 gtt1 mL=20 gtt/min.60\
\text{mL/hr}\times\dfrac{1\ \text{hr}}{60\
\text{min}}\times\dfrac{20\ \text{gtt}}{1\ \text{mL}} = 20\
\text{gtt/min}.60 mL/hr×60 min1 hr×1 mL20 gtt=20 gtt/min.
Cancel hr and mL units. Compute: 60÷60=160\div60=160÷60=1
mL/min; 1×20=201\times20=201×20=20 gtt/min.
Rationale — A: (10) likely from halving the drop factor or
dividing by 120 instead of 60 — common arithmetic error.
Rationale — B: (60) reflects multiplying 60 mL/hr directly by 1
gtt/mL (forgetting drop factor) — unit error.
Rationale — D: (40) suggests using a 40 gtt/mL factor by
mistake — wrong tubing factor.
Teaching point: Always convert hours → minutes (÷60) before
applying gtt/mL.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
