Answer :
To solve this problem, we need to find the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles, each weighing [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
1. Identify the Weight of One Particle:
A single dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
2. Identify the Number of Particles:
We have [tex]\(5 \times 10^6\)[/tex] dust particles.
3. Calculate the Total Weight:
To find the total weight of the dust particles, multiply the weight of one particle by the total number of particles:
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
4. Perform the Multiplication:
When multiplying numbers in scientific notation, multiply the coefficients (7.42 and 5) and add the exponents of 10:
- Multiply the coefficients: [tex]\(7.42 \times 5 = 37.1\)[/tex]
- Add the exponents: [tex]\((-10) + 6 = -4\)[/tex]
So, the total weight can be expressed in scientific notation as:
[tex]\[
37.1 \times 10^{-4} \, \text{kilograms}
\][/tex]
Therefore, the correct answer is:
D. [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms
1. Identify the Weight of One Particle:
A single dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
2. Identify the Number of Particles:
We have [tex]\(5 \times 10^6\)[/tex] dust particles.
3. Calculate the Total Weight:
To find the total weight of the dust particles, multiply the weight of one particle by the total number of particles:
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
4. Perform the Multiplication:
When multiplying numbers in scientific notation, multiply the coefficients (7.42 and 5) and add the exponents of 10:
- Multiply the coefficients: [tex]\(7.42 \times 5 = 37.1\)[/tex]
- Add the exponents: [tex]\((-10) + 6 = -4\)[/tex]
So, the total weight can be expressed in scientific notation as:
[tex]\[
37.1 \times 10^{-4} \, \text{kilograms}
\][/tex]
Therefore, the correct answer is:
D. [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms
