Question

which of the following quantities is equivalent to 3.7 cm? answer: a ( 3.7 \times 10^{-3} ) m b ( 3.7 \times 10^{-5} ) km c ( 3.7 \times 10^{-2} ) mm d ( 3.7 \times 10^{5} ) μm

Explanation:

Step1: Recall unit conversion factors

We know the following unit conversions:

• \(1\space cm = 10^{-2}\space m\)
• \(1\space cm = 10^{-5}\space km\)
• \(1\space cm = 10\space mm\)
• \(1\space cm = 10^{4}\space \mu m\)

Step2: Convert \(3.7\space cm\) to each unit

• Option A: Convert \(3.7\space cm\) to meters.

Since \(1\space cm = 10^{-2}\space m\), then \(3.7\space cm = 3.7\times10^{-2}\space m\). But option A is \(3.7\times 10^{-3}\space m\), so A is incorrect.

• Option B: Convert \(3.7\space cm\) to kilometers.

Since \(1\space cm = 10^{-5}\space km\), then \(3.7\space cm = 3.7\times10^{-5}\space km\). This matches option B. Let's check other options to be sure.

• Option C: Convert \(3.7\space cm\) to millimeters.

Since \(1\space cm = 10\space mm\), then \(3.7\space cm = 3.7\times10\space mm=3.7\times 10^{1}\space mm\). Option C is \(3.7\times 10^{-2}\space mm\), so C is incorrect.

• Option D: Convert \(3.7\space cm\) to micrometers.

Since \(1\space cm = 10^{4}\space \mu m\), then \(3.7\space cm = 3.7\times10^{4}\space \mu m\). Option D is \(3.7\times 10^{5}\space \mu m\), so D is incorrect.

Answer:

B. \(3.7\times 10^{-5}\space km\)