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Answer :
To find the total weight of the dust particles, we'll follow these steps:
1. Determine the weight of a single dust particle:
The problem states that a single dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
2. Determine the number of dust particles:
We're looking at a total of [tex]\(5 \times 10^{6}\)[/tex] dust particles.
3. Calculate the total weight of the dust particles:
To find the total weight, multiply the weight of a single dust particle by the total number of particles:
[tex]\[
7.42 \times 10^{-10} \text{ kg} \times 5 \times 10^{6} = 3.71 \times 10^{-3} \text{ kg}
\][/tex]
This multiplication involves multiplying the coefficients (7.42 and 5) and adding the exponents of 10 (-10 and 6):
[tex]\[
(7.42 \times 5) \times (10^{-10 + 6}) = 37.1 \times 10^{-4} \text{ kg}
\][/tex]
Simplifying the scientific notation, [tex]\(37.1 \times 10^{-4}\)[/tex] can be expressed as [tex]\(3.71 \times 10^{-3}\)[/tex] kg.
4. Select the correct answer:
From the given options, the total weight of the dust particles in scientific notation is:
[tex]\[
B. \: 3.71 \times 10^{-3} \text{ kilograms}
\][/tex]
So the correct answer is B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
1. Determine the weight of a single dust particle:
The problem states that a single dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
2. Determine the number of dust particles:
We're looking at a total of [tex]\(5 \times 10^{6}\)[/tex] dust particles.
3. Calculate the total weight of the dust particles:
To find the total weight, multiply the weight of a single dust particle by the total number of particles:
[tex]\[
7.42 \times 10^{-10} \text{ kg} \times 5 \times 10^{6} = 3.71 \times 10^{-3} \text{ kg}
\][/tex]
This multiplication involves multiplying the coefficients (7.42 and 5) and adding the exponents of 10 (-10 and 6):
[tex]\[
(7.42 \times 5) \times (10^{-10 + 6}) = 37.1 \times 10^{-4} \text{ kg}
\][/tex]
Simplifying the scientific notation, [tex]\(37.1 \times 10^{-4}\)[/tex] can be expressed as [tex]\(3.71 \times 10^{-3}\)[/tex] kg.
4. Select the correct answer:
From the given options, the total weight of the dust particles in scientific notation is:
[tex]\[
B. \: 3.71 \times 10^{-3} \text{ kilograms}
\][/tex]
So the correct answer is B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
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