Certainly! Let's go through the process of multiplying the given numbers expressed in scientific notation step-by-step:
Given:
[tex]\[
\left(9.16 \times 10^{-3}\right)\left(5.5 \times 10^6\right)
\][/tex]
1. Multiply the coefficients:
[tex]\[
9.16 \times 5.5 = 50.38
\][/tex]
2. Multiply the powers of 10:
[tex]\[
10^{-3} \times 10^6 = 10^{-3+6} = 10^3
\][/tex]
3. Combine the results:
[tex]\[
50.38 \times 10^3
\][/tex]
4. Convert the result to proper scientific notation:
Scientific notation typically keeps the coefficient between 1 and 10. Therefore, we convert:
[tex]\[
50.38 \times 10^3
\][/tex]
to
[tex]\[
5.038 \times 10^{4}
\][/tex]
This is done by moving the decimal point one place to the left and increasing the exponent by 1.
Thus, the product expressed in scientific notation is:
[tex]\[
5.038 \times 10^4
\][/tex]
So, the correct choice from the given options is:
[tex]\[
5.038 \times 10^4
\][/tex]
