Answer :
To find the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation, follow these steps:
1. Multiply the bases:
Multiply 8.2 and 4.5.
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the exponents:
Since both numbers are powers of 10, you can add their exponents.
[tex]\[
10^9 \times 10^{-5} = 10^{9 + (-5)} = 10^4
\][/tex]
3. Combine the results:
Combine the results from steps 1 and 2 into scientific notation.
[tex]\[
36.9 \times 10^4
\][/tex]
4. Adjust the number to fit scientific notation:
In scientific notation, the base number should be between 1 and 10. To achieve this, adjust [tex]\(36.9\)[/tex] to [tex]\(3.69\)[/tex] and increase the exponent by 1 (since you moved the decimal one place to the left):
[tex]\[
3.69 \times 10^5
\][/tex]
Thus, the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] is [tex]\(3.69 \times 10^5\)[/tex], which matches with one of the given options.
1. Multiply the bases:
Multiply 8.2 and 4.5.
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the exponents:
Since both numbers are powers of 10, you can add their exponents.
[tex]\[
10^9 \times 10^{-5} = 10^{9 + (-5)} = 10^4
\][/tex]
3. Combine the results:
Combine the results from steps 1 and 2 into scientific notation.
[tex]\[
36.9 \times 10^4
\][/tex]
4. Adjust the number to fit scientific notation:
In scientific notation, the base number should be between 1 and 10. To achieve this, adjust [tex]\(36.9\)[/tex] to [tex]\(3.69\)[/tex] and increase the exponent by 1 (since you moved the decimal one place to the left):
[tex]\[
3.69 \times 10^5
\][/tex]
Thus, the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] is [tex]\(3.69 \times 10^5\)[/tex], which matches with one of the given options.