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Answer :
To determine the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles, each weighing [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms, you should follow these steps:
1. Identify the weight of a single particle:
- A single dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
2. Identify the number of particles:
- There are [tex]\(5 \times 10^6\)[/tex] particles.
3. Calculate the total weight:
- Multiply the weight of one particle by the total number of particles:
[tex]\[
(7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
4. Multiply the coefficients:
- Multiply 7.42 by 5:
[tex]\[
7.42 \times 5 = 37.1
\][/tex]
5. Address the exponents in scientific notation:
- Add the exponents of 10:
[tex]\[
10^{-10} \times 10^6 = 10^{-4}
\][/tex]
6. Combine the results:
- The product is [tex]\(37.1 \times 10^{-4}\)[/tex].
7. Adjust to proper scientific notation:
- Move the decimal point one place to the left:
[tex]\[
37.1 \times 10^{-4} = 3.71 \times 10^{-3}
\][/tex]
The correct answer is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms, which corresponds to option B.
1. Identify the weight of a single particle:
- A single dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
2. Identify the number of particles:
- There are [tex]\(5 \times 10^6\)[/tex] particles.
3. Calculate the total weight:
- Multiply the weight of one particle by the total number of particles:
[tex]\[
(7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
4. Multiply the coefficients:
- Multiply 7.42 by 5:
[tex]\[
7.42 \times 5 = 37.1
\][/tex]
5. Address the exponents in scientific notation:
- Add the exponents of 10:
[tex]\[
10^{-10} \times 10^6 = 10^{-4}
\][/tex]
6. Combine the results:
- The product is [tex]\(37.1 \times 10^{-4}\)[/tex].
7. Adjust to proper scientific notation:
- Move the decimal point one place to the left:
[tex]\[
37.1 \times 10^{-4} = 3.71 \times 10^{-3}
\][/tex]
The correct answer is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms, which corresponds to option B.
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