Answer :
To find the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation, let's break it down into step-by-step instructions.
1. Multiply the coefficients:
We need to multiply the numerical parts [tex]\(8.2\)[/tex] and [tex]\(4.5\)[/tex].
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the exponents of 10:
Since we are multiplying numbers in scientific notation, we add the exponents. We have [tex]\(10^9\)[/tex] and [tex]\(10^{-5}\)[/tex].
[tex]\[
9 + (-5) = 4
\][/tex]
3. Combine the results:
Now, we put our multiplied coefficient and the sum of the exponents together to express it in scientific notation.
[tex]\[
36.9 \times 10^4
\][/tex]
So, the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation is [tex]\(36.9 \times 10^4\)[/tex]. However, in scientific notation, we generally prefer the coefficient to be between 1 and 10. In this case, since 36.9 is not between 1 and 10, we could rewrite it as [tex]\(3.69 \times 10^5\)[/tex].
Therefore, the correct answer is [tex]\(\boxed{3.69 \times 10^5}\)[/tex].
1. Multiply the coefficients:
We need to multiply the numerical parts [tex]\(8.2\)[/tex] and [tex]\(4.5\)[/tex].
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the exponents of 10:
Since we are multiplying numbers in scientific notation, we add the exponents. We have [tex]\(10^9\)[/tex] and [tex]\(10^{-5}\)[/tex].
[tex]\[
9 + (-5) = 4
\][/tex]
3. Combine the results:
Now, we put our multiplied coefficient and the sum of the exponents together to express it in scientific notation.
[tex]\[
36.9 \times 10^4
\][/tex]
So, the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation is [tex]\(36.9 \times 10^4\)[/tex]. However, in scientific notation, we generally prefer the coefficient to be between 1 and 10. In this case, since 36.9 is not between 1 and 10, we could rewrite it as [tex]\(3.69 \times 10^5\)[/tex].
Therefore, the correct answer is [tex]\(\boxed{3.69 \times 10^5}\)[/tex].
