Answer :
To solve this problem, we need to calculate the total weight of [tex]$5 \times 10^6$[/tex] dust particles, each weighing [tex]$7.42 \times 10^{-10}$[/tex] kilograms. Here's how you can do it step-by-step:
1. Understand the Problem: You have the weight of one dust particle and the number of dust particles. You need to find the total weight for all these particles combined.
2. Multiply the Weight by the Number of Particles:
- The weight of one dust particle is [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
- The number of dust particles is [tex]\(5 \times 10^6\)[/tex].
3. Calculation:
- Multiply the weight of one particle by the total number of particles:
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
- To multiply these numbers, you multiply the coefficients (7.42 and 5) and add the exponents of 10:
[tex]\[
7.42 \times 5 = 37.1
\][/tex]
[tex]\[
10^{-10} \times 10^6 = 10^{-4}
\][/tex]
- Combine these results:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
4. Convert to Standard Scientific Notation:
- The expression [tex]\(37.1 \times 10^{-4}\)[/tex] is not in standard scientific notation because the coefficient is not between 1 and 10.
- To convert, move the decimal point one place to the left and adjust the exponent of 10:
[tex]\[
3.71 \times 10^{-3}
\][/tex]
5. Conclusion: The total weight of [tex]$5 \times 10^6$[/tex] dust particles is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
Thus, the correct answer is B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
1. Understand the Problem: You have the weight of one dust particle and the number of dust particles. You need to find the total weight for all these particles combined.
2. Multiply the Weight by the Number of Particles:
- The weight of one dust particle is [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
- The number of dust particles is [tex]\(5 \times 10^6\)[/tex].
3. Calculation:
- Multiply the weight of one particle by the total number of particles:
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
- To multiply these numbers, you multiply the coefficients (7.42 and 5) and add the exponents of 10:
[tex]\[
7.42 \times 5 = 37.1
\][/tex]
[tex]\[
10^{-10} \times 10^6 = 10^{-4}
\][/tex]
- Combine these results:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
4. Convert to Standard Scientific Notation:
- The expression [tex]\(37.1 \times 10^{-4}\)[/tex] is not in standard scientific notation because the coefficient is not between 1 and 10.
- To convert, move the decimal point one place to the left and adjust the exponent of 10:
[tex]\[
3.71 \times 10^{-3}
\][/tex]
5. Conclusion: The total weight of [tex]$5 \times 10^6$[/tex] dust particles is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
Thus, the correct answer is B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
