Scale, Proportion, and Quantity Flashcards

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?

Answer: 50 meters

Multiply the model measurement by the scale factor: 0.5 m × 100 = 50 meters.

Which unit of measurement would be most appropriate for expressing the diameter of an atom?

Answer: Nanometers (nm)

Atoms are typically 0.1–0.5 nm in diameter, making nanometers the appropriate unit for atomic-scale measurements.

A scientist measures a bacterial cell and finds it is 0.002 mm in diameter. Written in scientific notation, this measurement is:

Answer: 2 × 10⁻³ mm

0.002 mm = 2 × 10⁻³ mm; scientific notation requires exactly one non-zero digit before the decimal point.

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?

Answer: 300 km

Multiply the map distance by the scale factor: 6 cm × 50 km/cm = 300 km.

Which of the following correctly arranges these lengths from smallest to largest: 1 km, 1 cm, 1 mm, 1 m?

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.

When scientists say that Earth's age is on the order of 10⁹ years, they mean Earth is approximately:

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.

Which of the following best represents a directly proportional relationship between two variables?

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.