Dimensional Analysis Practice
Quantitative Skills · Units
New numbers every set.
Choose one skill for 8 questions, or Mixed review for 12. Every set has new numbers.
No timer. Use scratch paper and a calculator. The method from the lesson is below.
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Dimensional analysis
- Map the path first: write the starting unit and the goal, with one factor per step.
- Chain the factors so each bottom unit cancels the top unit before it: 1.5 h × (60 min / 1 h) × (60 s / 1 min) = 5400 s.
- Rates: convert one unit at a time. Hours are on the bottom of km/h, so h goes on top: 90.0 km/h × (1000 m / 1 km) × (1 h / 3600 s) = 25.0 m/s.
- Squared and cubed units: square or cube the whole factor, numbers and units. (100 cm / 1 m)³ gives 1 m³ = 1,000,000 cm³, and 1 m² = 10,000 cm².
- 1 cm³ = 1 mL exactly: 0.355 L = 355 mL = 355 cm³.
- Let the units check the setup: m/s × s gives m, but m/s ÷ s gives m/s², so that setup is wrong.
- The factors are exact, so the answer keeps the measurement's significant figures. When zeros at the end would be unclear, use scientific notation: 2.50 d = 3.60 × 103 min.
Practice for the Dimensional Analysis lesson in Quantitative Skills. Original ZornScience questions.
About this activity
Chain conversion factors across several steps, convert rates and densities, and square or cube factors for area and volume. Every set has new numbers, and each answer gets feedback right away.
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