Answer :
To find the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles, each weighing [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms, we need to multiply the weight of one dust particle by the number of particles.
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. Multiply the weight of one particle by the number of particles:
[tex]\[
(7.42 \times 10^{-10}) \times (5 \times 10^6) = 37.1 \times 10^{-4} \text{ kilograms}
\][/tex]
4. Convert to scientific notation (simplify if necessary):
The result can be written as [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms by adjusting the decimal place.
So, the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms. The correct answer is option 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. Multiply the weight of one particle by the number of particles:
[tex]\[
(7.42 \times 10^{-10}) \times (5 \times 10^6) = 37.1 \times 10^{-4} \text{ kilograms}
\][/tex]
4. Convert to scientific notation (simplify if necessary):
The result can be written as [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms by adjusting the decimal place.
So, the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms. The correct answer is option B: [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
