To solve the given multiplication and express the result in scientific notation, we'll follow these steps:
1. Break down the expression:
We are given:
[tex]\[
8.365 \times 10^3 \times 1.2 \times 10^{-9}
\][/tex]
2. Rearrange and group the coefficients and the powers of 10:
Group the coefficients (8.365 and 1.2) and the powers of 10 ([tex]\(10^3\)[/tex] and [tex]\(10^{-9}\)[/tex]) separately:
[tex]\[
(8.365 \times 1.2) \times (10^3 \times 10^{-9})
\][/tex]
3. Multiply the coefficients:
[tex]\[
8.365 \times 1.2 = 10.038
\][/tex]
4. Combine the powers of 10 using the properties of exponents:
[tex]\[
10^3 \times 10^{-9} = 10^{3 + (-9)} = 10^{-6}
\][/tex]
5. Combine the results:
Now, write the product of the coefficients with the result from the powers of 10:
[tex]\[
10.038 \times 10^{-6}
\][/tex]
6. Adjust the coefficient to standard form in scientific notation if needed:
Scientific notation requires the coefficient to be a number between 1 and 10. In this case, 10.038 needs adjustment:
[tex]\[
10.038 = 1.0038 \times 10^1
\][/tex]
7. Combine this adjusted coefficient with the power of 10:
[tex]\[
1.0038 \times 10^1 \times 10^{-6} = 1.0038 \times 10^{1 + (-6)} = 1.0038 \times 10^{-5}
\][/tex]
Therefore, the final answer in scientific notation is:
[tex]\[
1.0038 \times 10^{-5}
\][/tex]
So, performing the operation [tex]\(8.365 \times 10^3 \times 1.2 \times 10^{-9}\)[/tex] and expressing the result in scientific notation yields:
[tex]\[
1.0038 \times 10^{-5}
\][/tex]
