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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 coefficients (numbers in front):
- Multiply [tex]\(8.2\)[/tex] by [tex]\(4.5\)[/tex] to get [tex]\(36.9\)[/tex].
2. Add the exponents (powers of 10):
- The exponents are [tex]\(9\)[/tex] and [tex]\(-5\)[/tex].
- Add these exponents: [tex]\(9 + (-5) = 4\)[/tex].
3. Combine the results:
- The product is [tex]\(36.9 \times 10^4\)[/tex].
4. Convert to proper scientific notation:
- Scientific notation requires a coefficient between 1 and 10.
- Convert [tex]\(36.9\)[/tex] to [tex]\(3.69\)[/tex] by moving the decimal one place to the left.
- Since we moved the decimal one place to the left, increase the exponent by 1: [tex]\(10^4\)[/tex] becomes [tex]\(10^5\)[/tex].
So, 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 choice [tex]\(3.69 \times 10^5\)[/tex].
1. Multiply the coefficients (numbers in front):
- Multiply [tex]\(8.2\)[/tex] by [tex]\(4.5\)[/tex] to get [tex]\(36.9\)[/tex].
2. Add the exponents (powers of 10):
- The exponents are [tex]\(9\)[/tex] and [tex]\(-5\)[/tex].
- Add these exponents: [tex]\(9 + (-5) = 4\)[/tex].
3. Combine the results:
- The product is [tex]\(36.9 \times 10^4\)[/tex].
4. Convert to proper scientific notation:
- Scientific notation requires a coefficient between 1 and 10.
- Convert [tex]\(36.9\)[/tex] to [tex]\(3.69\)[/tex] by moving the decimal one place to the left.
- Since we moved the decimal one place to the left, increase the exponent by 1: [tex]\(10^4\)[/tex] becomes [tex]\(10^5\)[/tex].
So, 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 choice [tex]\(3.69 \times 10^5\)[/tex].
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