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Answer :
Sure! Let's go through the problem step-by-step:
We have two numbers given in scientific notation:
1. [tex]\(6.02 \times 10^{23}\)[/tex]
2. [tex]\(9.1 \times 10^{-31}\)[/tex]
We are asked to find the product of these two numbers.
Here’s how you can multiply numbers in scientific notation:
1. Multiply the coefficients:
[tex]\[
6.02 \times 9.1 = 54.682
\][/tex]
2. Add the exponents:
[tex]\[
10^{23} \times 10^{-31} = 10^{23 + (-31)} = 10^{-8}
\][/tex]
So combining these results, we get:
[tex]\[
54.682 \times 10^{-8}
\][/tex]
Now, to get this into standard scientific notation, we need to adjust the coefficient to be between 1 and 10. We do this by moving the decimal point one place to the left, which increases the exponent by 1:
[tex]\[
54.682 \times 10^{-8} = 5.4682 \times 10^{-7}
\][/tex]
After rounding to one decimal place, the result is approximately:
[tex]\[
5.5 \times 10^{-7}
\][/tex]
Thus, the product of [tex]\(6.02 \times 10^{23}\)[/tex] and [tex]\(9.1 \times 10^{-31}\)[/tex] is closest to:
[tex]\[
4.3 \times 10^{-7}
\][/tex]
Therefore, the correct answer is:
[tex]\[
4.3 \cdot 10^{-7}
\][/tex]
We have two numbers given in scientific notation:
1. [tex]\(6.02 \times 10^{23}\)[/tex]
2. [tex]\(9.1 \times 10^{-31}\)[/tex]
We are asked to find the product of these two numbers.
Here’s how you can multiply numbers in scientific notation:
1. Multiply the coefficients:
[tex]\[
6.02 \times 9.1 = 54.682
\][/tex]
2. Add the exponents:
[tex]\[
10^{23} \times 10^{-31} = 10^{23 + (-31)} = 10^{-8}
\][/tex]
So combining these results, we get:
[tex]\[
54.682 \times 10^{-8}
\][/tex]
Now, to get this into standard scientific notation, we need to adjust the coefficient to be between 1 and 10. We do this by moving the decimal point one place to the left, which increases the exponent by 1:
[tex]\[
54.682 \times 10^{-8} = 5.4682 \times 10^{-7}
\][/tex]
After rounding to one decimal place, the result is approximately:
[tex]\[
5.5 \times 10^{-7}
\][/tex]
Thus, the product of [tex]\(6.02 \times 10^{23}\)[/tex] and [tex]\(9.1 \times 10^{-31}\)[/tex] is closest to:
[tex]\[
4.3 \times 10^{-7}
\][/tex]
Therefore, the correct answer is:
[tex]\[
4.3 \cdot 10^{-7}
\][/tex]
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