AZSCI Scale, Proportion, and Quantity 1 — Questions and Answers
Question 1: A scale model of a building uses a ratio of 1:100. If the model is 0.5 meters tall, how tall is the actual building?
- 50 meters (Correct answer)
- 5 meters
- 500 meters
- 0.05 meters
Correct answer: 50 meters
Multiply the model measurement by the scale factor: 0.5 m × 100 = 50 meters.
Question 2: Which unit of measurement would be most appropriate for expressing the diameter of an atom?
- Nanometers (nm) (Correct answer)
- Millimeters (mm)
- Centimeters (cm)
- Meters (m)
Correct answer: Nanometers (nm)
Atoms are typically 0.1–0.5 nm in diameter, making nanometers the appropriate unit for atomic-scale measurements.
Question 3: A scientist measures a bacterial cell and finds it is 0.002 mm in diameter. Written in scientific notation, this measurement is:
- 2 × 10⁻³ mm (Correct answer)
- 2 × 10³ mm
- 0.2 × 10⁻² mm
- 20 × 10⁻⁴ mm
Correct answer: 2 × 10⁻³ mm
0.002 mm = 2 × 10⁻³ mm; scientific notation requires exactly one non-zero digit before the decimal point.
Question 4: If a map has a scale of 1 cm = 50 km, and two cities are 6 cm apart on the map, what is the actual distance between them?
- 300 km (Correct answer)
- 56 km
- 30 km
- 3,000 km
Correct answer: 300 km
Multiply the map distance by the scale factor: 6 cm × 50 km/cm = 300 km.
Question 5: Which of the following correctly arranges these lengths from smallest to largest: 1 km, 1 cm, 1 mm, 1 m?
- 1 mm, 1 cm, 1 m, 1 km (Correct answer)
- 1 cm, 1 mm, 1 m, 1 km
- 1 mm, 1 m, 1 cm, 1 km
- 1 km, 1 m, 1 cm, 1 mm
Correct answer: 1 mm, 1 cm, 1 m, 1 km
1 mm < 1 cm < 1 m < 1 km; each unit is 10× or 1000× larger than the previous.
Question 6: When scientists say that Earth's age is on the order of 10⁹ years, they mean Earth is approximately:
- 1 billion years old (Correct answer)
- 1 million years old
- 1 trillion years old
- 100 million years old
Correct answer: 1 billion years old
10⁹ = 1,000,000,000 = 1 billion, so an order of magnitude of 10⁹ years means approximately 1 billion years.
Question 7: Which of the following best represents a directly proportional relationship between two variables?
- As one variable doubles, the other also doubles (Correct answer)
- As one variable doubles, the other stays the same
- As one variable doubles, the other triples
- As one variable increases, the other randomly changes
Correct answer: As one variable doubles, the other also doubles
A directly proportional relationship means both variables change by the same factor, so when one doubles, the other doubles as well.
AZSCI Scale, Proportion, and Quantity 1
A scale model of a building uses a ratio of 1:100.
If the model is 0.5 meters tall, how tall is the actual building?