Answer :
We are given that one dust particle weighs
[tex]$$7.42 \times 10^{-10} \text{ kilograms},$$[/tex]
and we have
[tex]$$5 \times 10^6$$[/tex]
dust particles. The total weight is found by multiplying the weight of one particle by the total number of particles:
[tex]$$
\text{Total weight} = \left(7.42 \times 10^{-10}\right) \times \left(5 \times 10^6\right).
$$[/tex]
Step 1: Multiply the coefficients:
Multiply 7.42 by 5:
[tex]$$
7.42 \times 5 = 37.1.
$$[/tex]
Step 2: Combine the powers of 10:
Multiply the powers of 10 by adding their exponents:
[tex]$$
10^{-10} \times 10^6 = 10^{-10+6} = 10^{-4}.
$$[/tex]
So the intermediate result is:
[tex]$$
37.1 \times 10^{-4} \text{ kilograms}.
$$[/tex]
Step 3: Express in standard scientific notation:
In proper scientific notation, the coefficient should be between 1 and 10. Here, 37.1 is greater than 10. We can adjust it by rewriting:
[tex]$$
37.1 \times 10^{-4} = 3.71 \times 10 \times 10^{-4} = 3.71 \times 10^{-3}.
$$[/tex]
Thus, the total weight of [tex]$5 \times 10^6$[/tex] dust particles is:
[tex]$$
3.71 \times 10^{-3} \text{ kilograms}.
$$[/tex]
The correct answer is option B.
[tex]$$7.42 \times 10^{-10} \text{ kilograms},$$[/tex]
and we have
[tex]$$5 \times 10^6$$[/tex]
dust particles. The total weight is found by multiplying the weight of one particle by the total number of particles:
[tex]$$
\text{Total weight} = \left(7.42 \times 10^{-10}\right) \times \left(5 \times 10^6\right).
$$[/tex]
Step 1: Multiply the coefficients:
Multiply 7.42 by 5:
[tex]$$
7.42 \times 5 = 37.1.
$$[/tex]
Step 2: Combine the powers of 10:
Multiply the powers of 10 by adding their exponents:
[tex]$$
10^{-10} \times 10^6 = 10^{-10+6} = 10^{-4}.
$$[/tex]
So the intermediate result is:
[tex]$$
37.1 \times 10^{-4} \text{ kilograms}.
$$[/tex]
Step 3: Express in standard scientific notation:
In proper scientific notation, the coefficient should be between 1 and 10. Here, 37.1 is greater than 10. We can adjust it by rewriting:
[tex]$$
37.1 \times 10^{-4} = 3.71 \times 10 \times 10^{-4} = 3.71 \times 10^{-3}.
$$[/tex]
Thus, the total weight of [tex]$5 \times 10^6$[/tex] dust particles is:
[tex]$$
3.71 \times 10^{-3} \text{ kilograms}.
$$[/tex]
The correct answer is option B.
