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 Decimal Parts:
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the Exponents:
For the powers of 10, you add the exponents:
[tex]\[
10^9 \times 10^{-5} = 10^{(9 + -5)} = 10^4
\][/tex]
3. Combine the Results:
Now, combine the product of the decimal parts with the product of the powers of 10:
[tex]\[
36.9 \times 10^4
\][/tex]
4. Convert to Standard Scientific Notation:
Scientific notation requires the decimal part to be between 1 and 10, so adjust [tex]\(36.9\)[/tex] by moving the decimal point one place to the left, to get [tex]\(3.69\)[/tex], and then increase the exponent by 1 to compensate:
[tex]\[
3.69 \times 10^{4+1} = 3.69 \times 10^5
\][/tex]
In conclusion, 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 the choice given: [tex]\(3.69 \times 10^5\)[/tex].
1. Multiply the Decimal Parts:
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the Exponents:
For the powers of 10, you add the exponents:
[tex]\[
10^9 \times 10^{-5} = 10^{(9 + -5)} = 10^4
\][/tex]
3. Combine the Results:
Now, combine the product of the decimal parts with the product of the powers of 10:
[tex]\[
36.9 \times 10^4
\][/tex]
4. Convert to Standard Scientific Notation:
Scientific notation requires the decimal part to be between 1 and 10, so adjust [tex]\(36.9\)[/tex] by moving the decimal point one place to the left, to get [tex]\(3.69\)[/tex], and then increase the exponent by 1 to compensate:
[tex]\[
3.69 \times 10^{4+1} = 3.69 \times 10^5
\][/tex]
In conclusion, 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 the choice given: [tex]\(3.69 \times 10^5\)[/tex].