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Answer :
Sure, let's solve this step-by-step.
We are asked to find the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex].
### Step 1: Multiply the coefficients
First, multiply the coefficients [tex]\(8.2\)[/tex] and [tex]\(4.5\)[/tex]:
[tex]\[ 8.2 \times 4.5 = 36.9 \][/tex]
### Step 2: Add the exponents
Next, add the exponents of [tex]\(10\)[/tex]:
[tex]\[ 9 + (-5) = 4 \][/tex]
### Step 3: Combine the results
Combine the coefficient from Step 1 and the sum of the exponents from Step 2:
[tex]\[ 36.9 \times 10^4 \][/tex]
However, scientific notation typically requires the coefficient to be between 1 and 10.
To adjust 36.9 into proper scientific notation, we rewrite it:
[tex]\[ 36.9 = 3.69 \times 10^1 \][/tex]
So, we combine this adjustment with the exponent [tex]\(4\)[/tex]:
[tex]\[ 3.69 \times 10^1 \times 10^4 = 3.69 \times 10^{1+4} = 3.69 \times 10^5 \][/tex]
### Conclusion
Therefore, 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]
This matches the provided answer:
[tex]\[ \boxed{3.69 \times 10^5} \][/tex]
We are asked to find the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex].
### Step 1: Multiply the coefficients
First, multiply the coefficients [tex]\(8.2\)[/tex] and [tex]\(4.5\)[/tex]:
[tex]\[ 8.2 \times 4.5 = 36.9 \][/tex]
### Step 2: Add the exponents
Next, add the exponents of [tex]\(10\)[/tex]:
[tex]\[ 9 + (-5) = 4 \][/tex]
### Step 3: Combine the results
Combine the coefficient from Step 1 and the sum of the exponents from Step 2:
[tex]\[ 36.9 \times 10^4 \][/tex]
However, scientific notation typically requires the coefficient to be between 1 and 10.
To adjust 36.9 into proper scientific notation, we rewrite it:
[tex]\[ 36.9 = 3.69 \times 10^1 \][/tex]
So, we combine this adjustment with the exponent [tex]\(4\)[/tex]:
[tex]\[ 3.69 \times 10^1 \times 10^4 = 3.69 \times 10^{1+4} = 3.69 \times 10^5 \][/tex]
### Conclusion
Therefore, 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]
This matches the provided answer:
[tex]\[ \boxed{3.69 \times 10^5} \][/tex]
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