Dimensional Analysis
Calculating Dosages Safely
3rd Edition
• Author(s)Tracy Horntvedt
TEST BANK
1
Reference: Ch. 1 — Whole Numbers — Dividing Whole
Numbers
Stem: The provider orders acetaminophen 900 mg PO now. On
hand: acetaminophen 300 mg tablets. Using dimensional
analysis, how many tablets will you administer?
A. 2 tablets
B. 3 tablets
C. 4 tablets
D. 1 tablet
Correct answer: B. 3 tablets
,Rationales
• Correct (B): Setup:
900 mg (ordered)300 mg/tablet (on hand)=3 tablets
\frac{900\ \text{mg (ordered)}}{300\ \text{mg/tablet (on
hand)}} = 3\
\text{tablets}300 mg/tablet (on hand)900 mg (ordered)
=3 tablets. Units cancel (mg → tablets). No rounding
required. Safe and straightforward.
• A (2 tablets): Error: Dividing incorrectly (e.g., 900 ÷ 300 ≈ 3
but student truncated to 2) — underdosing.
• C (4 tablets): Error: Multiplication instead of division (300
× 4 = 1200 mg) — overdosing.
• D (1 tablet): Error: Off-by-one underestimation; likely
thinking “one tablet” rather than performing the division.
Teaching point: Always set up ordered unit over on-hand unit to
cancel units cleanly.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
2
Reference: Ch. 1 — Whole Numbers — Subtracting Whole
Numbers
Stem: The nurse starts with 24 oral morphine sulfate tablets.
The patient receives 3 tablets every day for 5 days. Using
,dimensional analysis, how many tablets remain in the
medication drawer?
A. 6 tablets
B. 9 tablets
C. 15 tablets
D. 12 tablets
Correct answer: B. 9 tablets
Rationales
• Correct (B): Total given = 3 tablets/day×5 days=153\
\text{tablets/day} \times 5\ \text{days} =
153 tablets/day×5 days=15 tablets. Remaining =
24−15=924 - 15 = 924−15=9 tablets. Multi-step: multiply
then subtract.
• A (6 tablets): Error: Student may have done 24−(3×6)24 -
(3 \times 6)24−(3×6) or used wrong days. Underdosed
calculation for inventory.
• C (15 tablets): Error: Mistakenly reporting total
administered rather than remaining.
• D (12 tablets): Error: Possibly did 24−1224 - 1224−12
assuming 2 tablets/day; incorrect frequency.
Teaching point: Multiply frequency × days before subtracting
from starting inventory.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
, 3
Reference: Ch. 1 — Whole Numbers — Dividing Whole
Numbers
Stem: The provider orders 1,000 mL of maintenance IV fluids
over 8 hours. The infusion pump requires mL/hr. Using
dimensional analysis, what rate do you program?
A. 80 mL/hr
B. 125 mL/hr
C. 112 mL/hr
D. 150 mL/hr
Correct answer: B. 125 mL/hr
Rationales
• Correct (B): Setup: 1000 mL8 hr=125 mL/hr \frac{1000\
\text{mL}}{8\ \text{hr}} = 125\ \text{mL/hr}8 hr1000 mL
=125 mL/hr. Units cancel (mL ÷ hr). No rounding.
• A (80 mL/hr): Error: Dividing by wrong time (e.g., 12 hr).
• C (112 mL/hr): Error: Arithmetic error (1000 ÷ 8 = 125, not
112).
• D (150 mL/hr): Error: Student may have approximated or
used 6.66 hr mistakenly.
Teaching point: Divide total volume by total hours; keep units in
numerator/denominator straight.
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
Stem: The provider orders acetaminophen 900 mg PO now. On
hand: acetaminophen 300 mg tablets. Using dimensional
analysis, how many tablets will you administer?
A. 2 tablets
B. 3 tablets
C. 4 tablets
D. 1 tablet
Correct answer: B. 3 tablets
,Rationales
• Correct (B): Setup:
900 mg (ordered)300 mg/tablet (on hand)=3 tablets
\frac{900\ \text{mg (ordered)}}{300\ \text{mg/tablet (on
hand)}} = 3\
\text{tablets}300 mg/tablet (on hand)900 mg (ordered)
=3 tablets. Units cancel (mg → tablets). No rounding
required. Safe and straightforward.
• A (2 tablets): Error: Dividing incorrectly (e.g., 900 ÷ 300 ≈ 3
but student truncated to 2) — underdosing.
• C (4 tablets): Error: Multiplication instead of division (300
× 4 = 1200 mg) — overdosing.
• D (1 tablet): Error: Off-by-one underestimation; likely
thinking “one tablet” rather than performing the division.
Teaching point: Always set up ordered unit over on-hand unit to
cancel units cleanly.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
2
Reference: Ch. 1 — Whole Numbers — Subtracting Whole
Numbers
Stem: The nurse starts with 24 oral morphine sulfate tablets.
The patient receives 3 tablets every day for 5 days. Using
,dimensional analysis, how many tablets remain in the
medication drawer?
A. 6 tablets
B. 9 tablets
C. 15 tablets
D. 12 tablets
Correct answer: B. 9 tablets
Rationales
• Correct (B): Total given = 3 tablets/day×5 days=153\
\text{tablets/day} \times 5\ \text{days} =
153 tablets/day×5 days=15 tablets. Remaining =
24−15=924 - 15 = 924−15=9 tablets. Multi-step: multiply
then subtract.
• A (6 tablets): Error: Student may have done 24−(3×6)24 -
(3 \times 6)24−(3×6) or used wrong days. Underdosed
calculation for inventory.
• C (15 tablets): Error: Mistakenly reporting total
administered rather than remaining.
• D (12 tablets): Error: Possibly did 24−1224 - 1224−12
assuming 2 tablets/day; incorrect frequency.
Teaching point: Multiply frequency × days before subtracting
from starting inventory.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
, 3
Reference: Ch. 1 — Whole Numbers — Dividing Whole
Numbers
Stem: The provider orders 1,000 mL of maintenance IV fluids
over 8 hours. The infusion pump requires mL/hr. Using
dimensional analysis, what rate do you program?
A. 80 mL/hr
B. 125 mL/hr
C. 112 mL/hr
D. 150 mL/hr
Correct answer: B. 125 mL/hr
Rationales
• Correct (B): Setup: 1000 mL8 hr=125 mL/hr \frac{1000\
\text{mL}}{8\ \text{hr}} = 125\ \text{mL/hr}8 hr1000 mL
=125 mL/hr. Units cancel (mL ÷ hr). No rounding.
• A (80 mL/hr): Error: Dividing by wrong time (e.g., 12 hr).
• C (112 mL/hr): Error: Arithmetic error (1000 ÷ 8 = 125, not
112).
• D (150 mL/hr): Error: Student may have approximated or
used 6.66 hr mistakenly.
Teaching point: Divide total volume by total hours; keep units in
numerator/denominator straight.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
