Answer :
To find the weight of [tex]\(5 \times 10^6\)[/tex] dust particles, each weighing [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms, you can follow these steps:
1. Identify the problem components:
- Each dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
- You need to find the total weight for [tex]\(5 \times 10^6\)[/tex] dust particles.
2. Set up the multiplication:
- Multiply the weight of a single particle by the number of particles:
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
3. Multiply the coefficients:
- Multiply the numbers (7.42 and 5):
[tex]\[
7.42 \times 5 = 37.1
\][/tex]
4. Add the exponents of 10:
- Since you're multiplying powers of 10, add the exponents:
[tex]\[
10^{-10} \times 10^6 = 10^{-10 + 6} = 10^{-4}
\][/tex]
5. Combine the results:
- Combine the result from the coefficient multiplication with the power of ten:
[tex]\[
\text{Total weight} = 37.1 \times 10^{-4}
\][/tex]
6. Express in proper scientific notation:
- Scientific notation typically expresses the number with one non-zero digit before the decimal. So, [tex]\(37.1 \times 10^{-4}\)[/tex] can be adjusted to:
[tex]\[
3.71 \times 10^{-3}
\][/tex]
Therefore, the weight of [tex]\(5 \times 10^6\)[/tex] dust particles is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms. The correct answer is:
B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms
1. Identify the problem components:
- Each dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
- You need to find the total weight for [tex]\(5 \times 10^6\)[/tex] dust particles.
2. Set up the multiplication:
- Multiply the weight of a single particle by the number of particles:
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
3. Multiply the coefficients:
- Multiply the numbers (7.42 and 5):
[tex]\[
7.42 \times 5 = 37.1
\][/tex]
4. Add the exponents of 10:
- Since you're multiplying powers of 10, add the exponents:
[tex]\[
10^{-10} \times 10^6 = 10^{-10 + 6} = 10^{-4}
\][/tex]
5. Combine the results:
- Combine the result from the coefficient multiplication with the power of ten:
[tex]\[
\text{Total weight} = 37.1 \times 10^{-4}
\][/tex]
6. Express in proper scientific notation:
- Scientific notation typically expresses the number with one non-zero digit before the decimal. So, [tex]\(37.1 \times 10^{-4}\)[/tex] can be adjusted to:
[tex]\[
3.71 \times 10^{-3}
\][/tex]
Therefore, the weight of [tex]\(5 \times 10^6\)[/tex] dust particles is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms. The correct answer is:
B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms
