Answer :
To find the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles, each weighing [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms, follow these steps:
1. Understand the Problem:
You need to multiply the weight of one dust particle by the number of particles to get the total weight.
2. Write Down the Known Values:
- Weight of one dust particle: [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms
- Number of dust particles: [tex]\(5 \times 10^6\)[/tex]
3. Calculate the Total Weight:
- Multiply the weight of one particle by the total number of particles:
[tex]\[
(7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
4. Use Properties of Exponents:
- When you multiply numbers in scientific notation, you multiply their coefficients (the numbers in front) and add their exponents.
- Multiply the coefficients: [tex]\(7.42 \times 5 = 37.1\)[/tex]
- Add the exponents of 10: [tex]\(-10 + 6 = -4\)[/tex]
5. Combine the Results:
- The total weight in scientific notation is:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
- This can be rewritten to standard scientific notation as:
[tex]\[
3.71 \times 10^{-3}
\][/tex]
6. Select the Correct Answer:
- The total weight of the dust particles is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms, which corresponds to option B.
Therefore, the correct answer is B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
1. Understand the Problem:
You need to multiply the weight of one dust particle by the number of particles to get the total weight.
2. Write Down the Known Values:
- Weight of one dust particle: [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms
- Number of dust particles: [tex]\(5 \times 10^6\)[/tex]
3. Calculate the Total Weight:
- Multiply the weight of one particle by the total number of particles:
[tex]\[
(7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
4. Use Properties of Exponents:
- When you multiply numbers in scientific notation, you multiply their coefficients (the numbers in front) and add their exponents.
- Multiply the coefficients: [tex]\(7.42 \times 5 = 37.1\)[/tex]
- Add the exponents of 10: [tex]\(-10 + 6 = -4\)[/tex]
5. Combine the Results:
- The total weight in scientific notation is:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
- This can be rewritten to standard scientific notation as:
[tex]\[
3.71 \times 10^{-3}
\][/tex]
6. Select the Correct Answer:
- The total weight of the dust particles is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms, which corresponds to option B.
Therefore, the correct answer is B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
