Answer :
To find the total weight of the dust particles, we start with the weight of one particle and multiply it by the total number of particles.
1. The weight of one particle is
[tex]$$7.42 \times 10^{-10} \, \text{kg}.$$[/tex]
2. The number of particles is
[tex]$$5 \times 10^6.$$[/tex]
3. Multiply the two values:
[tex]$$\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6).$$[/tex]
4. Multiply the numerical coefficients and add the exponents:
[tex]$$7.42 \times 5 = 37.1,$$[/tex]
and
[tex]$$-10 + 6 = -4.$$[/tex]
So,
[tex]$$\text{Total weight} = 37.1 \times 10^{-4} \, \text{kg}.$$[/tex]
5. To express the answer in proper scientific notation, we adjust the coefficient so that it is between 1 and 10. Since
[tex]$$37.1 = 3.71 \times 10,$$[/tex]
we can write:
[tex]$$37.1 \times 10^{-4} = 3.71 \times 10 \times 10^{-4} = 3.71 \times 10^{-3} \, \text{kg}.$$[/tex]
Thus, the weight of the [tex]$5 \times 10^6$[/tex] dust particles is
[tex]$$\boxed{3.71 \times 10^{-3} \, \text{kg}}.$$[/tex]
1. The weight of one particle is
[tex]$$7.42 \times 10^{-10} \, \text{kg}.$$[/tex]
2. The number of particles is
[tex]$$5 \times 10^6.$$[/tex]
3. Multiply the two values:
[tex]$$\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6).$$[/tex]
4. Multiply the numerical coefficients and add the exponents:
[tex]$$7.42 \times 5 = 37.1,$$[/tex]
and
[tex]$$-10 + 6 = -4.$$[/tex]
So,
[tex]$$\text{Total weight} = 37.1 \times 10^{-4} \, \text{kg}.$$[/tex]
5. To express the answer in proper scientific notation, we adjust the coefficient so that it is between 1 and 10. Since
[tex]$$37.1 = 3.71 \times 10,$$[/tex]
we can write:
[tex]$$37.1 \times 10^{-4} = 3.71 \times 10 \times 10^{-4} = 3.71 \times 10^{-3} \, \text{kg}.$$[/tex]
Thus, the weight of the [tex]$5 \times 10^6$[/tex] dust particles is
[tex]$$\boxed{3.71 \times 10^{-3} \, \text{kg}}.$$[/tex]
