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Answer :
To solve the problem of finding 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 decimal parts of the numbers:
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the exponents: Next, add the exponents of 10 from the numbers being multiplied:
[tex]\[
9 + (-5) = 4
\][/tex]
3. Combine the results: Multiply the result from step 1 by 10 raised to the power from step 2:
[tex]\[
36.9 \times 10^4
\][/tex]
4. Express in scientific notation: To express this in proper scientific notation, we should have only one non-zero digit before the decimal point. So, convert 36.9 into 3.69 and adjust the exponent accordingly:
[tex]\[
3.69 \times 10^5
\][/tex]
Therefore, the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation is [tex]\(\boxed{3.69 \times 10^5}\)[/tex].
1. Multiply the coefficients: First, multiply the decimal parts of the numbers:
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the exponents: Next, add the exponents of 10 from the numbers being multiplied:
[tex]\[
9 + (-5) = 4
\][/tex]
3. Combine the results: Multiply the result from step 1 by 10 raised to the power from step 2:
[tex]\[
36.9 \times 10^4
\][/tex]
4. Express in scientific notation: To express this in proper scientific notation, we should have only one non-zero digit before the decimal point. So, convert 36.9 into 3.69 and adjust the exponent accordingly:
[tex]\[
3.69 \times 10^5
\][/tex]
Therefore, the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation is [tex]\(\boxed{3.69 \times 10^5}\)[/tex].
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