Answer :
Sure! Let's solve this problem step by step.
We are given that one dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms. We need to find the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles.
1. Multiply the weight of one particle by the number of particles:
[tex]\[
\text{Total weight} = \left(7.42 \times 10^{-10} \, \text{kg}\right) \times \left(5 \times 10^6\right)
\][/tex]
2. Multiply these numbers together:
- First, multiply the coefficients: [tex]\(7.42 \times 5 = 37.1\)[/tex]
- Then, add the exponents: [tex]\(-10 + 6 = -4\)[/tex]
So, the scientific notation of the total weight is:
[tex]\[
37.1 \times 10^{-4} \, \text{kg}
\][/tex]
3. Look at the choices given and find the matching one:
A. [tex]\(3.71 \times 10^{-4}\)[/tex] kilograms
B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms
C. [tex]\(37.1 \times 10^{-3}\)[/tex] kilograms
D. [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms
The correct answer is:
D. [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms
Thus, the weight of [tex]\(5 \times 10^6\)[/tex] dust particles is [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
We are given that one dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms. We need to find the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles.
1. Multiply the weight of one particle by the number of particles:
[tex]\[
\text{Total weight} = \left(7.42 \times 10^{-10} \, \text{kg}\right) \times \left(5 \times 10^6\right)
\][/tex]
2. Multiply these numbers together:
- First, multiply the coefficients: [tex]\(7.42 \times 5 = 37.1\)[/tex]
- Then, add the exponents: [tex]\(-10 + 6 = -4\)[/tex]
So, the scientific notation of the total weight is:
[tex]\[
37.1 \times 10^{-4} \, \text{kg}
\][/tex]
3. Look at the choices given and find the matching one:
A. [tex]\(3.71 \times 10^{-4}\)[/tex] kilograms
B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms
C. [tex]\(37.1 \times 10^{-3}\)[/tex] kilograms
D. [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms
The correct answer is:
D. [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms
Thus, the weight of [tex]\(5 \times 10^6\)[/tex] dust particles is [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
