Question

which of the following units is the smallest? choose one option a kilometer b meter c nanometer d centimeter

Explanation:

Step1: Recall unit conversions

We know the following conversions:

• \(1\) kilometer \(= 1000\) meters, so \(1\) meter \(=\frac{1}{1000}\) kilometer.
• \(1\) meter \( = 100\) centimeters, so \(1\) centimeter \(=\frac{1}{100}\) meter \( = 0.01\) meter.
• \(1\) meter \(= 10^{9}\) nanometers, so \(1\) nanometer \(=10^{-9}\) meters.

Step2: Compare the magnitudes

• For option A: Kilometer is a large unit, \(1\) kilometer \( = 1000\) meters.
• For option B: Meter is the base unit here, magnitude is \(1\) meter.
• For option C: Nanometer, \(1\) nanometer \(=10^{-9}\) meters, which is a very small fraction of a meter.
• For option D: Centimeter, \(1\) centimeter \( = 0.01\) meters.

Comparing the values in terms of meters: \(10^{-9}\) (nanometer) \(< 0.01\) (centimeter) \(< 1\) (meter) \(< 1000\) (kilometer).

Answer:

C. Nanometer