Answer :
Sure! Let's find the weight of [tex]\(5 \times 10^6\)[/tex] dust particles in scientific notation.
1. Understand the Problem:
- One dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
- We need to find the total weight of [tex]\(5 \times 10^6\)[/tex] particles.
2. Calculate the Total Weight:
- Multiply the weight of one dust particle by the number of particles:
[tex]\[
(7.42 \times 10^{-10} \text{ kg}) \times (5 \times 10^6)
\][/tex]
3. Perform the Multiplication:
- Multiply the numbers: [tex]\(7.42 \times 5 = 37.1\)[/tex].
- Add the exponents of 10: [tex]\((-10) + 6 = -4\)[/tex].
4. Combine the Results in Scientific Notation:
- The total weight is then [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
5. Express in Scientific Notation Correctly:
- To express [tex]\(37.1 \times 10^{-4}\)[/tex] in proper scientific notation:
[tex]\[
3.71 \times 10^{-3}
\][/tex]
So, the weight of [tex]\(5 \times 10^6\)[/tex] dust particles is [tex]\(\boxed{3.71 \times 10^{-3}}\)[/tex] kilograms, which matches option B.
1. Understand the Problem:
- One dust particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
- We need to find the total weight of [tex]\(5 \times 10^6\)[/tex] particles.
2. Calculate the Total Weight:
- Multiply the weight of one dust particle by the number of particles:
[tex]\[
(7.42 \times 10^{-10} \text{ kg}) \times (5 \times 10^6)
\][/tex]
3. Perform the Multiplication:
- Multiply the numbers: [tex]\(7.42 \times 5 = 37.1\)[/tex].
- Add the exponents of 10: [tex]\((-10) + 6 = -4\)[/tex].
4. Combine the Results in Scientific Notation:
- The total weight is then [tex]\(37.1 \times 10^{-4}\)[/tex] kilograms.
5. Express in Scientific Notation Correctly:
- To express [tex]\(37.1 \times 10^{-4}\)[/tex] in proper scientific notation:
[tex]\[
3.71 \times 10^{-3}
\][/tex]
So, the weight of [tex]\(5 \times 10^6\)[/tex] dust particles is [tex]\(\boxed{3.71 \times 10^{-3}}\)[/tex] kilograms, which matches option B.
