Certainly! Let's perform the multiplication step-by-step and then express the answer in scientific notation.
1. Identify the numbers to be multiplied:
We have [tex]\(8.20 \times 10^{-2}\)[/tex] and [tex]\(2.50 \times 10^6\)[/tex].
2. Multiply the coefficients (the numerical parts):
[tex]\[
8.20 \times 2.50 = 20.50
\][/tex]
3. Add the exponents:
When multiplying numbers in scientific notation, we add the exponents:
[tex]\[
(-2) + 6 = 4
\][/tex]
4. Combine the results:
Now, we can combine the multiplied coefficient and the sum of the exponents:
[tex]\[
20.50 \times 10^4
\][/tex]
5. Express in correct scientific notation:
Scientific notation requires that the coefficient be between 1 and 10. So we need to adjust [tex]\(20.50\)[/tex] to fit that requirement.
[tex]\[
20.50 = 2.05 \times 10^1
\][/tex]
Therefore,
[tex]\[
20.50 \times 10^4 = 2.05 \times 10^1 \times 10^4
\][/tex]
6. Combine the exponents once more:
[tex]\[
2.05 \times 10^{(1+4)} = 2.05 \times 10^5
\][/tex]
So, the result of the operation [tex]\(8.20 \times 10^{-2} \times 2.50 \times 10^6\)[/tex] expressed in correct scientific notation is:
[tex]\[
\boxed{2.05 \times 10^5}
\][/tex]
