Answer :
Sure! Let's solve this step-by-step:
1. Find the weight of one dust particle:
Each dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
2. Determine the number of dust particles:
We have [tex]\(5 \times 10^6\)[/tex] dust particles.
3. Calculate the total weight:
To find the total weight of these dust particles, we multiply the weight of one particle by the number of particles:
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10} \text{ kg}) \times (5 \times 10^6)
\][/tex]
4. Perform the multiplication:
First, multiply the numerical parts:
[tex]\(7.42 \times 5 = 37.1\)[/tex].
Next, handle the powers of 10:
[tex]\(10^{-10} \times 10^6 = 10^{-4}\)[/tex].
Combine these results to get:
[tex]\[
37.1 \times 10^{-4} \text{ kg}
\][/tex]
5. Express the result in scientific notation:
The weight of the [tex]$5 \times 10^6$[/tex] dust particles is [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
Hence, the correct answer is:
- D. [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms
1. Find the weight of one dust particle:
Each dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
2. Determine the number of dust particles:
We have [tex]\(5 \times 10^6\)[/tex] dust particles.
3. Calculate the total weight:
To find the total weight of these dust particles, we multiply the weight of one particle by the number of particles:
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10} \text{ kg}) \times (5 \times 10^6)
\][/tex]
4. Perform the multiplication:
First, multiply the numerical parts:
[tex]\(7.42 \times 5 = 37.1\)[/tex].
Next, handle the powers of 10:
[tex]\(10^{-10} \times 10^6 = 10^{-4}\)[/tex].
Combine these results to get:
[tex]\[
37.1 \times 10^{-4} \text{ kg}
\][/tex]
5. Express the result in scientific notation:
The weight of the [tex]$5 \times 10^6$[/tex] dust particles is [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
Hence, the correct answer is:
- D. [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms
