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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^{-3}[/tex] kilograms
B. [tex]3.71 \times 10^{-2}[/tex] kilograms
C. [tex]37.1 \times 10^{-2}[/tex] kilograms
D. [tex]37.1 \times 10^{-3}[/tex] kilograms

Answer :

Given:

Weight of one dust particle:

[tex]7.42\ast10^{10\text{ }}\operatorname{kg}[/tex]

Let's find the weight of:

[tex]5\ast10^6[/tex]

To find the weight of 5x10^6 dust particles, we have:

[tex]W=(5\ast10^6)\ast(7.42\ast10^{-10})[/tex]

Solving further:

[tex]\begin{gathered} W=5\ast7.42\ast10^{6-10} \\ \\ W=37.1\ast10^{-4} \\ \\ \text{Convert to scientific notation:} \\ W=3.71\ast10^{-3} \end{gathered}[/tex]

Therefore, the weight of 5x10^6 dust particles in scientific notation is:

[tex]3.71\ast10^{-3}[/tex]

ANSWER:

[tex]3.71\ast10^{-3}[/tex]

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