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Answer :
To find the weight of [tex]\(5 \times 10^6\)[/tex] dust particles, each weighing [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms, you'll need to multiply the weight of one particle by the total number of particles. Here's a detailed explanation of how to perform this calculation:
1. Identify the weight of one particle:
The weight of one dust particle is [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
2. Identify the number of particles:
There are [tex]\(5 \times 10^6\)[/tex] dust particles.
3. Calculate the total weight:
Multiply the weight of one particle by the number of particles:
[tex]\[
(7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
4. Perform the multiplication of coefficients:
[tex]\(7.42 \times 5 = 37.1\)[/tex].
5. Perform the multiplication of powers of ten:
[tex]\(10^{-10} \times 10^6 = 10^{-4}\)[/tex].
6. Combine the results:
Multiply the results from steps 4 and 5:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
7. Express the result in scientific notation:
The result [tex]\(37.1 \times 10^{-4}\)[/tex] is equivalent to [tex]\(3.71 \times 10^{-3}\)[/tex] when expressed in standard scientific notation by adjusting the decimal place.
So, the weight of [tex]\(5 \times 10^6\)[/tex] dust particles is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms. Therefore, the correct answer is:
B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
1. Identify the weight of one particle:
The weight of one dust particle is [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
2. Identify the number of particles:
There are [tex]\(5 \times 10^6\)[/tex] dust particles.
3. Calculate the total weight:
Multiply the weight of one particle by the number of particles:
[tex]\[
(7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
4. Perform the multiplication of coefficients:
[tex]\(7.42 \times 5 = 37.1\)[/tex].
5. Perform the multiplication of powers of ten:
[tex]\(10^{-10} \times 10^6 = 10^{-4}\)[/tex].
6. Combine the results:
Multiply the results from steps 4 and 5:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
7. Express the result in scientific notation:
The result [tex]\(37.1 \times 10^{-4}\)[/tex] is equivalent to [tex]\(3.71 \times 10^{-3}\)[/tex] when expressed in standard scientific notation by adjusting the decimal place.
So, the weight of [tex]\(5 \times 10^6\)[/tex] dust particles is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms. Therefore, the correct answer is:
B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
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