Question

A speck of dust is 5.0×10-⁷ squared millimeters wide. What is the best way to rewrite this quantity using more appropriate units?

A) 0.5 square micrometers
B) 50 square nanometers
C) 5 square millimeters
D) 500 square picometers

Answer 1

The area of the speck of dust, originally given in square millimeters, is best rewritten as 0.5 square micrometers after converting using a factor of 10^6.

Step-by-step explanation:

The question is asking to convert the area of a speck of dust from square millimeters to a more appropriate unit. The given area is 5.0×10^-7 square millimeters. To convert square millimeters to square micrometers (μm²), we multiply by a factor of 10^6 since there are 10^6 micrometers in a millimeter. Therefore, we have:

5.0×10^-7 mm² × 10^6 μm²/mm² = 5.0×10^-1 μm² = 0.5 μm².

Since square micrometers are a more commonly used unit for such tiny areas, the answer is 0.5 square micrometers or Option A. This makes the quantity much easier to understand and work with in practical scenarios, such as microscopy or particle physics.