Question

A speck of dust is 1.2 x 10-⁶ m wide. Which of the following is the best way to rewrite this quantity, using more appropriate units?

Options:
a) 1.2 x 10-³ mm
b) 1.2 x 10-⁶ m
c) 1.2 x 10-⁴ cm
d) 1.2 x 10-⁹ km

Answer 1

The correct answer is option a) 1.2 x 10-3 mm. The width of a speck of dust given as 1.2 x 10-6 meters is best rewritten in millimeters.

Step-by-step explanation:

To determine the most appropriate unit for the width of a speck of dust, we need to consider units that are commonly used to measure small lengths like these. The given size is 1.2 x 10-6 meters. Since one millimeter (mm) is equal to 10-3 meters, we can convert the speck of dust's width to millimeters by multiplying by 103 (which is the same as dividing by 10-3). This results in 1.2 x 10-6 m x 103 mm/m = 1.2 x 10-3 mm. Therefore, the width of the speck of dust is best rewritten as 1.2 x 10-3 millimeters, which is appropriate for measuring a small speck of dust.

To rewrite this quantity using more appropriate units, we need to use a unit that is smaller than meters. The prefix 'micro-' represents 10-6. So, the width of the speck of dust can be expressed as 1.2 micro meters or 1.2 μm.