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][tex]$3.71 \times 10^{-3}$[/tex][/tex] kilograms
C. [tex]$37.1 \times 10^{-3}$[/tex] kilograms
D. [tex]$37.1 \times 10^{-4}$[/tex] kilograms

Answer :

To find the total weight of the dust particles, we'll follow these steps:

1. Determine the weight of a single dust particle:
The problem states that a single dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.

2. Determine the number of dust particles:
We're looking at a total of [tex]\(5 \times 10^{6}\)[/tex] dust particles.

3. Calculate the total weight of the dust particles:
To find the total weight, multiply the weight of a single dust particle by the total number of particles:
[tex]\[
7.42 \times 10^{-10} \text{ kg} \times 5 \times 10^{6} = 3.71 \times 10^{-3} \text{ kg}
\][/tex]
This multiplication involves multiplying the coefficients (7.42 and 5) and adding the exponents of 10 (-10 and 6):
[tex]\[
(7.42 \times 5) \times (10^{-10 + 6}) = 37.1 \times 10^{-4} \text{ kg}
\][/tex]
Simplifying the scientific notation, [tex]\(37.1 \times 10^{-4}\)[/tex] can be expressed as [tex]\(3.71 \times 10^{-3}\)[/tex] kg.

4. Select the correct answer:
From the given options, the total weight of the dust particles in scientific notation is:
[tex]\[
B. \: 3.71 \times 10^{-3} \text{ kilograms}
\][/tex]

So the correct answer is B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.