Certainly, let's go through the detailed step-by-step solution to convert nanometers (nm) to meters (m).
Given that the radius of an atom is measured in nanometers, we need to find out how many meters are there in one nanometer.
1. Understanding the Conversion:
A nanometer is a unit of length in the metric system, equal to one billionth of a meter. Mathematically, it is represented as:
[tex]\[
1 \text{ nm} = \frac{1}{10^9} \text{ meters}
\][/tex]
2. Converting It to a Decimal Form:
Since the problem involves converting the unit into meters, we need to express the fraction [tex]\(\frac{1}{10^9}\)[/tex] as a decimal number. The expression [tex]\(\frac{1}{10^9}\)[/tex] can be written in scientific notation. Doing the conversion:
[tex]\[
\frac{1}{10^9} = 1 \times 10^{-9}
\][/tex]
3. Writing the Decimal (Standard) Form:
To write [tex]\(1 \times 10^{-9}\)[/tex] in a standard decimal form, move the decimal point nine places to the left of 1:
[tex]\[
0.000000001 \text{ meters}
\][/tex]
4. Final Result:
Thus, one nanometer is equal to:
[tex]\[
0.000000001 \text{ meters} \quad \text{or} \quad 1 \times 10^{-9} \text{ meters}
\][/tex]
5. Conclusion:
Therefore, 1 nanometer (nm) is equal to [tex]\(1 \times 10^{-9}\)[/tex] meters, which can also be represented as [tex]\(1e-9\)[/tex] meters in scientific notation.
So, when you measure the radius of an atom in nanometers and want to express that in meters, you can use the conversion factor:
[tex]\[
1 \text{ nm} = 1e-9 \text{ meters}
\][/tex]
This completes the detailed step-by-step conversion from nanometers to meters.
