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Answer :
To find the product of [tex]\(8.2 \times 10^9\)[/tex] and [tex]\(4.5 \times 10^{-5}\)[/tex] in scientific notation, follow these steps:
1. Multiply the significant figures (coefficients):
- First, multiply the numbers without considering the exponents:
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the exponents:
- When multiplying numbers in scientific notation, add the exponents of the powers of 10:
[tex]\[
10^9 \times 10^{-5} = 10^{9 + (-5)} = 10^4
\][/tex]
3. Combine the results:
- Combine the product of the coefficients and the summed exponents:
[tex]\[
36.9 \times 10^4
\][/tex]
Since scientific notation conventionally has a coefficient less than 10, rewrite [tex]\(36.9\)[/tex] as [tex]\(3.69 \times 10^1\)[/tex]. Thus, the scientific notation becomes:
4. Adjust to proper scientific notation:
- Split and adjust the coefficient if necessary:
[tex]\[
36.9 \times 10^4 = 3.69 \times 10^1 \times 10^4 = 3.69 \times 10^{1+4} = 3.69 \times 10^5
\][/tex]
Therefore, the product in scientific notation is [tex]\(\boxed{3.69 \times 10^5}\)[/tex].
1. Multiply the significant figures (coefficients):
- First, multiply the numbers without considering the exponents:
[tex]\[
8.2 \times 4.5 = 36.9
\][/tex]
2. Add the exponents:
- When multiplying numbers in scientific notation, add the exponents of the powers of 10:
[tex]\[
10^9 \times 10^{-5} = 10^{9 + (-5)} = 10^4
\][/tex]
3. Combine the results:
- Combine the product of the coefficients and the summed exponents:
[tex]\[
36.9 \times 10^4
\][/tex]
Since scientific notation conventionally has a coefficient less than 10, rewrite [tex]\(36.9\)[/tex] as [tex]\(3.69 \times 10^1\)[/tex]. Thus, the scientific notation becomes:
4. Adjust to proper scientific notation:
- Split and adjust the coefficient if necessary:
[tex]\[
36.9 \times 10^4 = 3.69 \times 10^1 \times 10^4 = 3.69 \times 10^{1+4} = 3.69 \times 10^5
\][/tex]
Therefore, the product in scientific notation is [tex]\(\boxed{3.69 \times 10^5}\)[/tex].
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