To express the diameter of a carbon atom, which is [tex]\(0.000000000154 \, m\)[/tex], in scientific notation, follow these steps:
1. Identify the non-zero digits in the number. Here, the non-zero digits are 1, 5, and 4, which make up the number 1.54.
2. Count the number of decimal places from the original number to where the decimal point would be if the number were written as [tex]\(1.54\)[/tex]. In other words, count how many places we have to move the decimal point to get from [tex]\(0.000000000154\)[/tex] to 1.54.
Moving the decimal point 10 places to the right:
[tex]\[
0.000000000154 \rightarrow 1.54
\][/tex]
3. Each movement of the decimal point to the right corresponds to a negative power of 10. Since we moved the decimal point 10 places to the right, we multiply [tex]\(1.54\)[/tex] by [tex]\(10^{-10}\)[/tex].
Thus, the number [tex]\(0.000000000154 \, m\)[/tex] expressed in scientific notation is [tex]\(1.54 \times 10^{-10} \, m\)[/tex].
Among the given options, the correct one is:
[tex]\[ 1.54 \times 10^{-10} \, m \][/tex]
