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What is the product of [tex]$8.2 \times 10^9$[/tex] and [tex]$4.5 \times 10^{-5}$[/tex] in scientific notation?

A. [tex]$36.9 \times 10^{-45}$[/tex]

B. [tex]$12.7 \times 10^4$[/tex]

C. [tex]$3.69 \times 10^5$[/tex]

D. [tex]$3.69 \times 10^{14}$[/tex]

Answer :

To find the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation, you can follow these steps:

1. Multiply the Coefficients:
- First, multiply the numerical (non-exponential) parts: [tex]\(8.2 \times 4.5\)[/tex].
- [tex]\(8.2 \times 4.5 = 36.9\)[/tex].

2. Add the Exponents:
- Next, add the exponents of the powers of 10. Here, you have [tex]\(10^9\)[/tex] and [tex]\(10^{-5}\)[/tex].
- Add the exponents: [tex]\(9 + (-5) = 4\)[/tex].

3. Combine the Results:
- Combine the coefficient from step 1 with the new power of 10 from step 2 to express the product in scientific notation.
- The result is [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]\(3.69 \times 10^5\)[/tex].

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