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 :

Sure! Let's find the weight of [tex]\(5 \times 10^6\)[/tex] dust particles in scientific notation.

1. Understand the Problem:
- 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] particles.

2. Calculate the Total Weight:
- Multiply the weight of one dust particle by the number of particles:
[tex]\[
(7.42 \times 10^{-10} \text{ kg}) \times (5 \times 10^6)
\][/tex]

3. Perform the Multiplication:
- Multiply the numbers: [tex]\(7.42 \times 5 = 37.1\)[/tex].
- Add the exponents of 10: [tex]\((-10) + 6 = -4\)[/tex].

4. Combine the Results in Scientific Notation:
- The total weight is then [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.

5. Express in Scientific Notation Correctly:
- To express [tex]\(37.1 \times 10^{-4}\)[/tex] in proper scientific notation:
[tex]\[
3.71 \times 10^{-3}
\][/tex]

So, the weight of [tex]\(5 \times 10^6\)[/tex] dust particles is [tex]\(\boxed{3.71 \times 10^{-3}}\)[/tex] kilograms, which matches option B.