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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]
[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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