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, follow these steps:
1. Understand the problem: We're given the weight of a single dust particle and the number of particles. We need to find the total weight of all the particles together.
2. Given values:
- Weight of one dust particle: [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms
- Number of dust particles: [tex]\(5 \times 10^6\)[/tex]
3. Calculate the total weight: Multiply the weight of one dust particle by the number of particles to get the total weight.
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10} \, \text{kg/particle}) \times (5 \times 10^6 \, \text{particles})
\][/tex]
4. Perform the multiplication:
- First, multiply the coefficients: [tex]\(7.42 \times 5 = 37.1\)[/tex].
- Then, multiply the powers of 10: [tex]\(10^{-10} \times 10^6 = 10^{-4}\)[/tex].
5. Combine the results:
[tex]\[
\text{Total weight} = 37.1 \times 10^{-4} \, \text{kg}
\][/tex]
6. Express in scientific notation:
[tex]\[
37.1 \times 10^{-4} \][/tex] is already in the format needed for scientific notation, matching option D.
Therefore, the weight of [tex]\(5 \times 10^6\)[/tex] dust particles is [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms. So, the correct answer is D. [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
1. Understand the problem: We're given the weight of a single dust particle and the number of particles. We need to find the total weight of all the particles together.
2. Given values:
- Weight of one dust particle: [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms
- Number of dust particles: [tex]\(5 \times 10^6\)[/tex]
3. Calculate the total weight: Multiply the weight of one dust particle by the number of particles to get the total weight.
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10} \, \text{kg/particle}) \times (5 \times 10^6 \, \text{particles})
\][/tex]
4. Perform the multiplication:
- First, multiply the coefficients: [tex]\(7.42 \times 5 = 37.1\)[/tex].
- Then, multiply the powers of 10: [tex]\(10^{-10} \times 10^6 = 10^{-4}\)[/tex].
5. Combine the results:
[tex]\[
\text{Total weight} = 37.1 \times 10^{-4} \, \text{kg}
\][/tex]
6. Express in scientific notation:
[tex]\[
37.1 \times 10^{-4} \][/tex] is already in the format needed for scientific notation, matching option D.
Therefore, the weight of [tex]\(5 \times 10^6\)[/tex] dust particles is [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms. So, the correct answer is D. [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
