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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 :

We start by multiplying the coefficients of the two numbers:

[tex]$$8.2 \times 4.5 = 36.9.$$[/tex]

Next, we add the exponents of the powers of 10:

[tex]$$10^9 \times 10^{-5} = 10^{9 + (-5)} = 10^4.$$[/tex]

At this stage, the product is written as:

[tex]$$36.9 \times 10^4.$$[/tex]

However, proper scientific notation requires the coefficient to be between 1 and 10. Since [tex]$36.9$[/tex] is greater than [tex]$10$[/tex], we can express it as:

[tex]$$36.9 = 3.69 \times 10^1.$$[/tex]

Substitute this back into the product:

[tex]$$36.9 \times 10^4 = \left(3.69 \times 10^1\right) \times 10^4.$$[/tex]

Combine the powers of 10 by adding the exponents:

[tex]$$3.69 \times 10^{1+4} = 3.69 \times 10^5.$$[/tex]

Thus, the final answer in scientific notation is:

[tex]$$\boxed{3.69 \times 10^5}.$$[/tex]

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