Question

A cell membrane is 7.0 nm thick. How thick is it in inches?

Short answer

The membrane is 2.756 × 10^-7 inches thick.

Step-by-step solution

Convert nanometers to meters

The thickness of the cell membrane is given as 7.0 nm. First, we need to convert nanometers (nm) into meters (m). Since 1 meter = \(10^9\) nanometers, we can convert as follows: \[7.0 \, \text{nm} = \frac{7.0}{10^9} \, \text{m} = 7.0 \times 10^{-9} \, \text{m}.\]

Convert meters to inches

Now that we have the thickness in meters, we convert it to inches. There are 39.3701 inches in a meter. Thus, multiply the thickness in meters by 39.3701 to convert: \[7.0 \times 10^{-9} \, \text{m} \times 39.3701 \, \text{inches/m} = 2.756 \times 10^{-7} \, \text{inches}.\]

Key concepts

Nanometers to Meters Conversion

When dealing with extremely small measurements like those in nanotechnology, it's common to use nanometers. Nanometers (nm) are one-billionth of a meter, which makes them perfect for measuring things like cell membranes. To convert from nanometers to meters, you need to understand that 1 meter equals 1,000,000,000 nanometers. So, if you're given a thickness in nanometers and need to find out how many meters that is, you simply divide the number of nanometers by 1,000,000,000 (
) or use scientific notation as shown:

• Given: 7.0 nm
• Conversion: \[ 7.0 \, \text{nm} = \frac{7.0}{10^9} \, \text{m} \]
• Result: \[ 7.0 \times 10^{-9} \, \text{m} \]

By converting nano-scale measurements to meters, it becomes easier to work with them in scientific calculations, allowing you to seamlessly shift scales and understand the relative size of microscopic structures.

Meters to Inches Conversion

Often, it's necessary to convert metric measurements to the imperial system, like when you're translating scientific data into a more familiar context for those in countries using imperial measurements. Here, we take the thickness already converted to meters and convert it to inches. This is crucial for contexts where imperial units are more prevalent.
The conversion factor is that there are 39.3701 inches in a meter. So, if you have a value in meters and you want to find out how many inches it is, you multiply that value by 39.3701. Let's see how it's done:

• Starting with \( 7.0 \times 10^{-9} \, \text{m} \)
• Conversion: \( 7.0 \times 10^{-9} \, \text{m} \times 39.3701 \, \text{inches/m} \)
• Result: \( 2.756 \times 10^{-7} \, \text{inches} \)

Converting meters to inches is a straightforward multiplication process that can make international communication and understanding of measurements more intuitive.

Cell Membrane Thickness Conversion

The thickness of a cell membrane is a tiny, yet critical measurement in biology and biotechnology. Knowing this can be essential for understanding cell function and structure.
The original measurement is often provided in nanometers because it is more practical to measure extremely small biological structures in smaller units.
In practical applications, converting a cell membrane's thickness into different units, like inches, might be necessary for broader communication. This allows scientists from different fields or regions to share consistent and understandable data.
By converting from 7.0 nm to inches, we see how the thickness appears in a more universally recognized form:

• 7.0 nm equals \(7.0 \times 10^{-9} \, \text{m} \) when converted to meters
• Converted to inches, this becomes \(2.756 \times 10^{-7} \, \text{inches} \)

This conversion demonstrates how versatile understanding unit conversions can be across different scientific and everyday scenarios.