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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. Identify what you know:
- The weight of one dust particle is [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
- You have [tex]\(5 \times 10^6\)[/tex] dust particles.
2. Multiply to find the total weight:
- To get the total weight of all the dust particles, multiply the weight of one particle by the number of particles:
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
3. Use properties of exponents:
- When you multiply two numbers in scientific notation, multiply their coefficients (the numbers in front) and add their exponents:
[tex]\[
7.42 \times 5 = 37.1
\][/tex]
[tex]\[
10^{-10} \times 10^6 = 10^{-10+6} = 10^{-4}
\][/tex]
4. Combine the results:
- The total weight of the dust particles, in scientific notation, is:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
Thus, the total weight of the dust particles is represented in scientific notation as [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms. Therefore, the correct answer is option D: [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
1. Identify what you know:
- The weight of one dust particle is [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
- You have [tex]\(5 \times 10^6\)[/tex] dust particles.
2. Multiply to find the total weight:
- To get the total weight of all the dust particles, multiply the weight of one particle by the number of particles:
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
3. Use properties of exponents:
- When you multiply two numbers in scientific notation, multiply their coefficients (the numbers in front) and add their exponents:
[tex]\[
7.42 \times 5 = 37.1
\][/tex]
[tex]\[
10^{-10} \times 10^6 = 10^{-10+6} = 10^{-4}
\][/tex]
4. Combine the results:
- The total weight of the dust particles, in scientific notation, is:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
Thus, the total weight of the dust particles is represented in scientific notation as [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms. Therefore, the correct answer is option D: [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
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