Questions on Dimensional Analysis
Multiple-Choice Questions – Dimensional Analysis
1. What is dimensional analysis primarily used for?
A) Balancing chemical equations
B) Solving algebra problems
C) Converting units
D) Analyzing atomic structure
E) Measuring density
2. Which of the following is an example of a conversion factor?
A) 1 + 1 = 2
B) 1 km = 1000 m
C) 5 m/s²
D) π × r²
E) 1 mole = 6.022 × 10²³
3. A conversion factor is always equal to:
A) 0
B) A variable
C) Infinity
D) 1
E) 100
4. In dimensional analysis, what does canceling units help you do?
A) Eliminate significant figures
B) Remove mathematical errors
C) Ensure correct units in the final answer
D) Increase the size of numbers
E) Round decimals
5. Which of the following is the correct conversion from 1 hour to seconds?
A) 1 hour = 60 seconds
B) 1 hour = 120 seconds
C) 1 hour = 3600 seconds
D) 1 hour = 600 seconds
E) 1 hour = 180 seconds
6. What is the first step in dimensional analysis?
A) Write the final answer
B) Choose random units
C) Identify the given quantity and its units
D) Multiply by 100
E) Guess the result
7. How many centimeters are in 1.5 meters?
A) 1.5 cm
B) 15 cm
C) 150 cm
D) 0.15 cm
E) 1500 cm
8. Convert 3.5 kilometers to meters.
A) 35 m
B) 0.35 m
C) 3500 m
D) 350 m
E) 3.5 m
9. A person drinks 2.5 liters of water. How many milliliters is this?
A) 250 mL
B) 2500 mL
C) 25 mL
D) 0.25 mL
E) 2.5 mL
10. Which of the following conversion factors would convert grams to kilograms?
A) 1 kg / 1000 g
B) 1000 g / 1 kg
C) 1 g / 1000 kg
D) 1 kg / 1 g
E) 1 g / 1000 g
11. If a car travels 60 miles per hour, how far does it travel in 2 hours?
A) 30 miles
B) 60 miles
C) 90 miles
D) 100 miles
E) 120 miles
12. Convert 1200 milligrams to grams.
A) 0.12 g
B) 1.2 g
C) 12 g
D) 120 g
E) 0.0012 g
13. Which of these is equivalent to 1 inch?
A) 1.54 cm
B) 2.54 cm
C) 3.54 cm
D) 4.54 cm
E) 0.54 cm
14. A conversion factor must always:
A) Be a whole number
B) Cancel all numbers
C) Represent an equality between two units
D) Change the identity of the substance
E) Contain the metric system
15. Convert 5 feet to inches (1 foot = 12 inches).
A) 50 inches
B) 48 inches
C) 60 inches
D) 24 inches
E) 72 inches
16. What unit results from multiplying speed (m/s) by time (s)?
A) m/s²
B) m/s
C) s²
D) m
E) kg
17. Convert 5000 mL to liters.
A) 50 L
B) 5 L
C) 0.5 L
D) 500 L
E) 0.05 L
18. What is the correct conversion of 98.6°F to Celsius?
A) 36°C
B) 40°C
C) 32°C
D) 37°C
E) 39°C
19. Which shows the correct setup for converting 60 minutes to hours?
A) 60 min × (1 hr / 30 min)
B) 60 min × (1 hr / 60 min)
C) 60 min × (60 hr / 1 min)
D) 60 min × (1 min / 60 hr)
E) 60 min × (1 hr / 120 min)
20. Which technique is essential in dimensional analysis?
A) Cross multiplication
B) Balancing equations
C) Using conversion factors as fractions
D) Scientific notation only
E) Drawing diagrams
- Questions on Mass and Weight
- Questions on Kinetic Energy
- Questions on Temperature and Temperature Scales
Answer Key with Explanations
1. C) Converting units
Dimensional analysis is mainly used to convert one unit into another.
2. B) 1 km = 1000 m
This is a conversion between two units of length.
3. D) 1
Conversion factors are equalities, so their ratio equals 1.
4. C) Ensure correct units in the final answer
Canceling units allows you to track the unit change properly.
5. C) 1 hour = 3600 seconds
1 hour = 60 minutes; 60 minutes = 3600 seconds.
6. C) Identify the given quantity and its units
You must know what you’re starting with before converting.
7. C) 150 cm
1 m = 100 cm, so 1.5 × 100 = 150 cm.
8. C) 3500 m
1 km = 1000 m → 3.5 × 1000 = 3500 m.
9. B) 2500 mL
1 L = 1000 mL → 2.5 × 1000 = 2500 mL.
10. A) 1 kg / 1000 g
This fraction cancels grams and gives the answer in kg.
11. E) 120 miles
60 miles/hour × 2 hours = 120 miles.
12. B) 1.2 g
1000 mg = 1 g → 1200 mg ÷ 1000 = 1.2 g.
13. B) 2.54 cm
This is the standard inch-to-centimeter conversion.
14. C) Represent an equality between two units
A conversion factor links two equivalent measurements.
15. C) 60 inches
5 feet × 12 inches = 60 inches.
16. D) m
(m/s) × s = m. Time cancels out.
17. B) 5 L
1000 mL = 1 L → 5000 ÷ 1000 = 5 L.
18. D) 37°C
Use: (°F - 32) × 5/9 = °C → (98.6 - 32) × 5/9 ≈ 37°C.
19. B) 60 min × (1 hr / 60 min)
Minutes cancel, leaving hours.
20. C) Using conversion factors as fractions
This is key to dimensional analysis and unit cancellation.
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