To determine how many centimeters one nanometer is equal to, we need to convert nanometers to centimeters.
First, let's understand the relationship between these units:
- A nanometer is [tex]\( 10^{-9} \)[/tex] meters.
- A centimeter is [tex]\( 10^{-2} \)[/tex] meters.
To convert nanometers to centimeters, we can follow these steps:
1. Convert Nanometers to Meters:
Since 1 nanometer (nm) is equal to [tex]\( 10^{-9} \)[/tex] meters (m), we start with:
[tex]\[
1 \, \text{nm} = 10^{-9} \, \text{m}
\][/tex]
2. Convert Meters to Centimeters:
Knowing that 1 meter is equal to 100 centimeters ([tex]\( 10^2 \)[/tex] cm), we can write:
[tex]\[
1 \, \text{m} = 10^2 \, \text{cm}
\][/tex]
Therefore, to convert meters to centimeters, we multiply meters by [tex]\( 10^2 \)[/tex]:
[tex]\[
10^{-9} \, \text{m} \times 10^2 \, \frac{\text{cm}}{\text{m}} = 10^{-7} \, \text{cm}
\][/tex]
Hence, one nanometer is equal to [tex]\( 10^{-7} \)[/tex] centimeters.
Therefore, the correct answer is:
C. [tex]\( 10^{-7} \, \text{cm} \)[/tex]
