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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 and the powers of ten separately.

1. Multiply the coefficients:
[tex]$$8.2 \times 4.5 = 36.9.$$[/tex]

2. Multiply the powers of ten by adding the exponents:
[tex]$$10^9 \times 10^{-5} = 10^{9 + (-5)} = 10^4.$$[/tex]

This gives us:
[tex]$$36.9 \times 10^4.$$[/tex]

3. The number must be expressed in proper scientific notation, where the coefficient is between 1 and 10. Since 36.9 is not between 1 and 10, we rewrite it by shifting the decimal point one place to the left:
[tex]$$36.9 \times 10^4 = 3.69 \times 10^5.$$[/tex]

Thus, the product in scientific notation is:
[tex]$$\boxed{3.69 \times 10^5}.$$[/tex]

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