1 nanometer is _________ centimeter.

A) 1e-8
B) 1e-7
C) 1e-9
D) 1e-6

1. Definition of Nanometer:
o 1 nanometer (1 nm1 \, \text{nm}) is equal to 10−910^{-9} meters.
2. Conversion from Meters to Centimeters:
o 1 m=100 cm1 \, \text{m} = 100 \, \text{cm}.
o Therefore, 1 nm=10−9 m=10−9×100 cm1 \, \text{nm} = 10^{-9} \, \text{m} = 10^{-9} \times 100 \, \text{cm}.
3. Simplify the Expression:
o 1 nm=10−7 cm1 \, \text{nm} = 10^{-7} \, \text{cm}.
Final Answer:
(B) 10−710^{-7}

To convert nanometers to centimeters, it's essential to understand the relationship between these units of measurement. A nanometer (nm) is one billionth of a meter, while a centimeter (cm) is one hundredth of a meter. This means that there are 10 million nanometers in a centimeter.

Conversion Process

To find out how many centimeters are in one nanometer, we can set up the conversion as follows:

• 1 nanometer = 1 x 10^-9 meters
• 1 centimeter = 1 x 10^-2 meters

Now, to convert nanometers to centimeters, we can use the following formula:

Centimeters = Nanometers × (1 cm / 10^-9 m) × (10^-2 m / 1 cm)

When we simplify this, we find:

1 nm = 1 x 10^-9 m × (1 cm / 10^-2 m) = 1 x 10^-9 / 10^-2 cm = 1 x 10^-7 cm

Final Answer

Therefore, 1 nanometer is equal to 1 x 10^-7 centimeters. Looking at the options provided:

• A) 1e-8
• B) 1e-7
• C) 1e-9
• D) 1e-6

The correct answer is B) 1e-7.

Understanding the Scale

To put this into perspective, consider that a human hair is about 80,000 to 100,000 nanometers wide. This illustrates just how small a nanometer really is compared to everyday objects. In scientific fields, especially in nanotechnology and materials science, understanding these conversions is crucial for working with materials at the atomic and molecular levels.