College

Select the correct answer.

A dust particle weighs [tex]7.42 \times 10^{-10}[/tex] kilograms. What is the weight of [tex]5 \times 10^6[/tex] dust particles represented in scientific notation?

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

Answer :

To find the weight of [tex]\(5 \times 10^6\)[/tex] dust particles, each weighing [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms, we need to multiply the weight of one particle by the total number of particles.

Here's the step-by-step calculation:

1. Weight of One Dust Particle:
[tex]\[
7.42 \times 10^{-10} \text{ kilograms}
\][/tex]

2. Number of Dust Particles:
[tex]\[
5 \times 10^6
\][/tex]

3. Total Weight Calculation:
- Multiply the weight of one dust particle by the number of particles:
[tex]\[
7.42 \times 10^{-10} \times 5 \times 10^6
\][/tex]

4. Breaking Down the Multiplication:
- First, multiply the coefficients: [tex]\(7.42 \times 5 = 37.1\)[/tex].
- Then, handle the powers of ten: [tex]\(10^{-10} \times 10^6 = 10^{-4}\)[/tex].
- Combine these results:
[tex]\[
37.1 \times 10^{-4}
\][/tex]

Thus, the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles is represented in scientific notation as:

[tex]\[
37.1 \times 10^{-4} \text{ kilograms}
\][/tex]

So, the correct answer is option D: [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.