Dimensional Analysis
Calculating Dosages Safely
3rd Edition
• Author(s)Tracy Horntvedt
TEST BANK
1)
Reference: Ch. 1 — Whole Numbers — Multiplying Whole
Numbers
Stem: A provider orders 900 mg of medication X PO. The unit
available is 300 mg tablets in a drawer. Using dimensional
analysis, how many tablets will you administer?
Options:
A. 2 tablets
B. 3 tablets
C. 4 tablets
D. 6 tablets
,Correct answer: B. 3 tablets
Rationale — Correct (B):
Setup: 900 mg×1 tablet300 mg=3 tablets900\ \text{mg} \times
\dfrac{1\ \text{tablet}}{300\ \text{mg}} = 3\
\text{tablets}900 mg×300 mg1 tablet=3 tablets. Unit mg
cancels, leaving tablets. Multiplication/division of whole
numbers yields 3 exactly. No rounding required; 3 tablets
matches the ordered 900 mg and is safe.
Rationale — A: 2 tablets results from 900÷300=3900 \div 300 =
3900÷300=3 misread as 2 — a subtraction/inversion error;
underdoses patient.
Rationale — C: 4 tablets arises from adding an extra tablet
(common careless addition). This yields 1200 mg — an
overdose.
Rationale — D: 6 tablets reflects doubling error (300 mg × 6 =
1800 mg), a multiplication mistake; unsafe.
Teaching point: Always set up factors so unwanted units cancel;
verify final unit equals tablets.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
2)
Reference: Ch. 1 — Whole Numbers — Dividing Whole
Numbers
Stem: An IV bag contains 1200 mL to infuse over 12 hours.
,Using dimensional analysis, what is the hourly infusion rate in
mL/hr to program the pump?
Options:
A. 80 mL/hr
B. 100 mL/hr
C. 120 mL/hr
D. 240 mL/hr
Correct answer: B. 100 mL/hr
Rationale — Correct (B):
Setup: 1200 mL÷12 hr=100 mL/hr1200\ \text{mL} \div 12\
\text{hr} = 100\ \text{mL/hr}1200 mL÷12 hr=100 mL/hr. Unit
cancellation: mL/hr results. Division of whole numbers yields
100—exact; pump programmed to 100 mL/hr is correct.
Rationale — A: 80 mL/hr is from 1200÷151200 \div 151200÷15
— using wrong time (15 hr) — a division error.
Rationale — C: 120 mL/hr suggests 1200÷101200 \div
101200÷10 — wrong divisor; would over-infuse.
Rationale — D: 240 mL/hr equals 1200÷51200 \div 51200÷5 —
major miscalculation and unsafe.
Teaching point: Confirm total volume and total time; divide
total volume by total hours.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
3)
, Reference: Ch. 1 — Whole Numbers — Adding Whole Numbers
Stem: A patient is prescribed 3 tablets of medication A in the
morning and 2 tablets in the evening. Each tablet is 50 mg.
Using dimensional analysis, what is the daily total mg the
patient receives?
Options:
A. 150 mg/day
B. 250 mg/day
C. 500 mg/day
D. 750 mg/day
Correct answer: B. 250 mg/day
Rationale — Correct (B):
Calculate tablets/day: 3+2=53 + 2 = 53+2=5 tablets/day. Then
convert: 5 tablets×50 mg/tablet=250 mg/day5\ \text{tablets}
\times 50\ \text{mg/tablet} = 250\
\text{mg/day}5 tablets×50 mg/tablet=250 mg/day. Units cancel
correctly; addition then multiplication of whole numbers yields
250 mg.
Rationale — A: 150 mg/day corresponds to 3×503 \times
503×50 only — omitted evening dose.
Rationale — C: 500 mg/day would be 10×5010 \times 5010×50
— doubling error in tablet count.
Rationale — D: 750 mg/day equals 15×5015 \times 5015×50 —
multiplication error; unsafe.
Teaching point: Sum doses in tablets first, then convert to mg to
avoid unit mistakes.
Calculating Dosages Safely
3rd Edition
• Author(s)Tracy Horntvedt
TEST BANK
1)
Reference: Ch. 1 — Whole Numbers — Multiplying Whole
Numbers
Stem: A provider orders 900 mg of medication X PO. The unit
available is 300 mg tablets in a drawer. Using dimensional
analysis, how many tablets will you administer?
Options:
A. 2 tablets
B. 3 tablets
C. 4 tablets
D. 6 tablets
,Correct answer: B. 3 tablets
Rationale — Correct (B):
Setup: 900 mg×1 tablet300 mg=3 tablets900\ \text{mg} \times
\dfrac{1\ \text{tablet}}{300\ \text{mg}} = 3\
\text{tablets}900 mg×300 mg1 tablet=3 tablets. Unit mg
cancels, leaving tablets. Multiplication/division of whole
numbers yields 3 exactly. No rounding required; 3 tablets
matches the ordered 900 mg and is safe.
Rationale — A: 2 tablets results from 900÷300=3900 \div 300 =
3900÷300=3 misread as 2 — a subtraction/inversion error;
underdoses patient.
Rationale — C: 4 tablets arises from adding an extra tablet
(common careless addition). This yields 1200 mg — an
overdose.
Rationale — D: 6 tablets reflects doubling error (300 mg × 6 =
1800 mg), a multiplication mistake; unsafe.
Teaching point: Always set up factors so unwanted units cancel;
verify final unit equals tablets.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
2)
Reference: Ch. 1 — Whole Numbers — Dividing Whole
Numbers
Stem: An IV bag contains 1200 mL to infuse over 12 hours.
,Using dimensional analysis, what is the hourly infusion rate in
mL/hr to program the pump?
Options:
A. 80 mL/hr
B. 100 mL/hr
C. 120 mL/hr
D. 240 mL/hr
Correct answer: B. 100 mL/hr
Rationale — Correct (B):
Setup: 1200 mL÷12 hr=100 mL/hr1200\ \text{mL} \div 12\
\text{hr} = 100\ \text{mL/hr}1200 mL÷12 hr=100 mL/hr. Unit
cancellation: mL/hr results. Division of whole numbers yields
100—exact; pump programmed to 100 mL/hr is correct.
Rationale — A: 80 mL/hr is from 1200÷151200 \div 151200÷15
— using wrong time (15 hr) — a division error.
Rationale — C: 120 mL/hr suggests 1200÷101200 \div
101200÷10 — wrong divisor; would over-infuse.
Rationale — D: 240 mL/hr equals 1200÷51200 \div 51200÷5 —
major miscalculation and unsafe.
Teaching point: Confirm total volume and total time; divide
total volume by total hours.
Citation: Horntvedt, T. (3rd ed.). Dimensional Analysis:
Calculating Dosages Safely. Ch. 1.
3)
, Reference: Ch. 1 — Whole Numbers — Adding Whole Numbers
Stem: A patient is prescribed 3 tablets of medication A in the
morning and 2 tablets in the evening. Each tablet is 50 mg.
Using dimensional analysis, what is the daily total mg the
patient receives?
Options:
A. 150 mg/day
B. 250 mg/day
C. 500 mg/day
D. 750 mg/day
Correct answer: B. 250 mg/day
Rationale — Correct (B):
Calculate tablets/day: 3+2=53 + 2 = 53+2=5 tablets/day. Then
convert: 5 tablets×50 mg/tablet=250 mg/day5\ \text{tablets}
\times 50\ \text{mg/tablet} = 250\
\text{mg/day}5 tablets×50 mg/tablet=250 mg/day. Units cancel
correctly; addition then multiplication of whole numbers yields
250 mg.
Rationale — A: 150 mg/day corresponds to 3×503 \times
503×50 only — omitted evening dose.
Rationale — C: 500 mg/day would be 10×5010 \times 5010×50
— doubling error in tablet count.
Rationale — D: 750 mg/day equals 15×5015 \times 5015×50 —
multiplication error; unsafe.
Teaching point: Sum doses in tablets first, then convert to mg to
avoid unit mistakes.
