Answer :
We start with the weight of one dust particle given as
[tex]$$
7.42 \times 10^{-10} \text{ kg}
$$[/tex]
and we have
[tex]$$
5 \times 10^{6}
$$[/tex]
dust particles.
To find the total weight, we multiply the weight of a single particle by the number of particles:
[tex]$$
\text{Total weight} = \left(7.42 \times 10^{-10}\right) \times \left(5 \times 10^{6}\right)
$$[/tex]
First, multiply the coefficients:
[tex]$$
7.42 \times 5 = 37.1
$$[/tex]
Next, add the exponents of the powers of 10:
[tex]$$
10^{-10} \times 10^{6} = 10^{-10+6} = 10^{-4}
$$[/tex]
Thus, the product becomes
[tex]$$
37.1 \times 10^{-4}.
$$[/tex]
To express this in proper scientific notation, we write the coefficient between 1 and 10. Notice that
[tex]$$
37.1 \times 10^{-4} = 3.71 \times 10^{-3},
$$[/tex]
since moving the decimal point one place to the left increases the exponent on 10 by 1.
Therefore, the weight of [tex]$5 \times 10^6$[/tex] dust particles is
[tex]$$
3.71 \times 10^{-3} \text{ kg}.
$$[/tex]
Comparing with the provided choices, the correct answer is:
[tex]$$
\boxed{3.71 \times 10^{-3} \text{ kilograms}}
$$[/tex].
[tex]$$
7.42 \times 10^{-10} \text{ kg}
$$[/tex]
and we have
[tex]$$
5 \times 10^{6}
$$[/tex]
dust particles.
To find the total weight, we multiply the weight of a single particle by the number of particles:
[tex]$$
\text{Total weight} = \left(7.42 \times 10^{-10}\right) \times \left(5 \times 10^{6}\right)
$$[/tex]
First, multiply the coefficients:
[tex]$$
7.42 \times 5 = 37.1
$$[/tex]
Next, add the exponents of the powers of 10:
[tex]$$
10^{-10} \times 10^{6} = 10^{-10+6} = 10^{-4}
$$[/tex]
Thus, the product becomes
[tex]$$
37.1 \times 10^{-4}.
$$[/tex]
To express this in proper scientific notation, we write the coefficient between 1 and 10. Notice that
[tex]$$
37.1 \times 10^{-4} = 3.71 \times 10^{-3},
$$[/tex]
since moving the decimal point one place to the left increases the exponent on 10 by 1.
Therefore, the weight of [tex]$5 \times 10^6$[/tex] dust particles is
[tex]$$
3.71 \times 10^{-3} \text{ kg}.
$$[/tex]
Comparing with the provided choices, the correct answer is:
[tex]$$
\boxed{3.71 \times 10^{-3} \text{ kilograms}}
$$[/tex].
