Dimensional Analysis
Calculating Dosages Safely
3rd Edition
• Author(s)Tracy Horntvedt
TEST BANK
1
Reference
Ch. 1 — Whole Numbers — Multiplying & Dividing Whole
Numbers
Stem
The provider orders acetaminophen 900 mg PO every 6 hours
for pain. The supply on the medication cart is 300 mg tablets.
Using dimensional analysis, how many tablets will the nurse
administer in a 24-hour period? (Assume full 24 hours.)
A. 8 tablets
B. 10 tablets
,C. 12 tablets
D. 16 tablets
Correct Answer: C
Rationales
Correct (C): Setup:
900 mg/dose×1 tablet300 mg=3 tablets/dose.900\
\text{mg/dose} \times \dfrac{1\ \text{tablet}}{300\ \text{mg}} =
3\ \text{tablets/dose}.900 mg/dose×300 mg1 tablet
=3 tablets/dose. Doses in 24 hr: 24÷6=424\div6=424÷6=4 →
3×4=123\times4=123×4=12 tablets. Units cancel properly (mg
→ tablets). Safe numeric result; no rounding needed.
A (8): Likely error: calculated 2 tablets/dose (900 ÷ 300 = 3) but
used 2; common misdivision. Unsafe under-dosing.
B (10): Likely error: used 5 doses/day (24÷6 rounded to 5)
instead of 4; misuse of time units. Results in extra tablets.
D (16): Likely error: multiplied 4 doses × 4 tablets (miscounting
tablets/dose), arithmetic slip. Would overdose.
Teaching Point: Always convert dose → tablets with mg/tablet,
then multiply by number of doses per time period.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
2
,Reference
Ch. 1 — Whole Numbers — Adding & Multiplying Whole
Numbers
Stem
The provider prescribes amoxicillin 500 mg PO every 8 hours
for 10 days. The supply is 500 mg tablets. How many tablets are
required to complete the 10-day course? Use dimensional
analysis.
A. 20 tablets
B. 30 tablets
C. 40 tablets
D. 50 tablets
Correct Answer: B
Rationales
Correct (B): Per dose: 500 mg×1 tab500 mg=1 tab/dose.500\
\text{mg}\times \dfrac{1\ \text{tab}}{500\ \text{mg}}=1\
\text{tab/dose}.500 mg×500 mg1 tab=1 tab/dose. Doses/day:
24÷8=324÷8=324÷8=3. Total tablets:
1×3×10=301\times3\times10=301×3×10=30. Units cancel
correctly.
A (20): Likely error: used 2 doses/day (24÷8 = 3) but miscounted
as 2. Underestimates supply.
C (40): Likely error: assumed 4 doses/day (24÷8 = 3 misapplied),
or 4 tabs/course/day ×10 =40. Overestimate.
D (50): Likely error: arithmetic error (5 tabs/day ×10). Unsafe
overstock but could prompt misuse.
, Teaching Point: Calculate tablets per dose, doses per day, then
multiply by days.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
3
Reference
Ch. 1 — Whole Numbers — Dividing Whole Numbers
Stem
A patient requires morphine 30 mg IM stat. The vial available is
10 mg/mL. Using dimensional analysis, how many mL should
the nurse withdraw?
A. 2 mL
B. 3 mL
C. 10 mL
D. 0.3 mL
Correct Answer: B
Rationales
Correct (B): Setup: 30 mg×1 mL10 mg=3 mL.30\
\text{mg}\times\dfrac{1\ \text{mL}}{10\ \text{mg}}=3\
\text{mL}.30 mg×10 mg1 mL=3 mL. Units cancel (mg → mL).
Simple division yields whole number; no rounding.
A (2 mL): Likely error: 30 ÷ 10 = 3 but student subtracted 1 mL
inadvertently—arithmetic slip. Under-dose risk.
Calculating Dosages Safely
3rd Edition
• Author(s)Tracy Horntvedt
TEST BANK
1
Reference
Ch. 1 — Whole Numbers — Multiplying & Dividing Whole
Numbers
Stem
The provider orders acetaminophen 900 mg PO every 6 hours
for pain. The supply on the medication cart is 300 mg tablets.
Using dimensional analysis, how many tablets will the nurse
administer in a 24-hour period? (Assume full 24 hours.)
A. 8 tablets
B. 10 tablets
,C. 12 tablets
D. 16 tablets
Correct Answer: C
Rationales
Correct (C): Setup:
900 mg/dose×1 tablet300 mg=3 tablets/dose.900\
\text{mg/dose} \times \dfrac{1\ \text{tablet}}{300\ \text{mg}} =
3\ \text{tablets/dose}.900 mg/dose×300 mg1 tablet
=3 tablets/dose. Doses in 24 hr: 24÷6=424\div6=424÷6=4 →
3×4=123\times4=123×4=12 tablets. Units cancel properly (mg
→ tablets). Safe numeric result; no rounding needed.
A (8): Likely error: calculated 2 tablets/dose (900 ÷ 300 = 3) but
used 2; common misdivision. Unsafe under-dosing.
B (10): Likely error: used 5 doses/day (24÷6 rounded to 5)
instead of 4; misuse of time units. Results in extra tablets.
D (16): Likely error: multiplied 4 doses × 4 tablets (miscounting
tablets/dose), arithmetic slip. Would overdose.
Teaching Point: Always convert dose → tablets with mg/tablet,
then multiply by number of doses per time period.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
2
,Reference
Ch. 1 — Whole Numbers — Adding & Multiplying Whole
Numbers
Stem
The provider prescribes amoxicillin 500 mg PO every 8 hours
for 10 days. The supply is 500 mg tablets. How many tablets are
required to complete the 10-day course? Use dimensional
analysis.
A. 20 tablets
B. 30 tablets
C. 40 tablets
D. 50 tablets
Correct Answer: B
Rationales
Correct (B): Per dose: 500 mg×1 tab500 mg=1 tab/dose.500\
\text{mg}\times \dfrac{1\ \text{tab}}{500\ \text{mg}}=1\
\text{tab/dose}.500 mg×500 mg1 tab=1 tab/dose. Doses/day:
24÷8=324÷8=324÷8=3. Total tablets:
1×3×10=301\times3\times10=301×3×10=30. Units cancel
correctly.
A (20): Likely error: used 2 doses/day (24÷8 = 3) but miscounted
as 2. Underestimates supply.
C (40): Likely error: assumed 4 doses/day (24÷8 = 3 misapplied),
or 4 tabs/course/day ×10 =40. Overestimate.
D (50): Likely error: arithmetic error (5 tabs/day ×10). Unsafe
overstock but could prompt misuse.
, Teaching Point: Calculate tablets per dose, doses per day, then
multiply by days.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
3
Reference
Ch. 1 — Whole Numbers — Dividing Whole Numbers
Stem
A patient requires morphine 30 mg IM stat. The vial available is
10 mg/mL. Using dimensional analysis, how many mL should
the nurse withdraw?
A. 2 mL
B. 3 mL
C. 10 mL
D. 0.3 mL
Correct Answer: B
Rationales
Correct (B): Setup: 30 mg×1 mL10 mg=3 mL.30\
\text{mg}\times\dfrac{1\ \text{mL}}{10\ \text{mg}}=3\
\text{mL}.30 mg×10 mg1 mL=3 mL. Units cancel (mg → mL).
Simple division yields whole number; no rounding.
A (2 mL): Likely error: 30 ÷ 10 = 3 but student subtracted 1 mL
inadvertently—arithmetic slip. Under-dose risk.
