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Answer :
To solve this problem, we need to determine the total weight of [tex]$5 \times 10^6$[/tex] dust particles, each weighing [tex]$7.42 \times 10^{-10}$[/tex] kilograms.
Here's a step-by-step guide on how to do this:
1. Understand the Problem:
- One dust particle weighs [tex]$7.42 \times 10^{-10}$[/tex] kilograms.
- We have [tex]$5 \times 10^6$[/tex] dust particles.
- We need to find the total weight of all these particles combined and express it in scientific notation.
2. Calculate the Total Weight:
- Multiply the weight of one dust particle by the total number of dust particles.
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
3. Perform the Multiplication:
- First, multiply the numbers: [tex]\(7.42 \times 5 = 37.1\)[/tex].
- Next, multiply the powers of ten: [tex]\(10^{-10} \times 10^6 = 10^{-10+6} = 10^{-4}\)[/tex].
4. Combine the Results:
- The total weight is [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
- In scientific notation, it's often more standard to express it with one digit before the decimal point, but here, [tex]\(37.1 \times 10^{-4}\)[/tex] is acceptable as a choice since we maintain the calculation setup.
5. Check the Options:
- The option matching this value is [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms, which is option D.
Therefore, the weight of [tex]$5 \times 10^6$[/tex] dust particles is [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
Here's a step-by-step guide on how to do this:
1. Understand the Problem:
- One dust particle weighs [tex]$7.42 \times 10^{-10}$[/tex] kilograms.
- We have [tex]$5 \times 10^6$[/tex] dust particles.
- We need to find the total weight of all these particles combined and express it in scientific notation.
2. Calculate the Total Weight:
- Multiply the weight of one dust particle by the total number of dust particles.
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
3. Perform the Multiplication:
- First, multiply the numbers: [tex]\(7.42 \times 5 = 37.1\)[/tex].
- Next, multiply the powers of ten: [tex]\(10^{-10} \times 10^6 = 10^{-10+6} = 10^{-4}\)[/tex].
4. Combine the Results:
- The total weight is [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
- In scientific notation, it's often more standard to express it with one digit before the decimal point, but here, [tex]\(37.1 \times 10^{-4}\)[/tex] is acceptable as a choice since we maintain the calculation setup.
5. Check the Options:
- The option matching this value is [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms, which is option D.
Therefore, the weight of [tex]$5 \times 10^6$[/tex] dust particles is [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
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