Answer :
To determine the weight of 5 dust particles when each particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms, follow these steps:
1. Understand the Problem: You have one dust particle weighing [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms, and you need to find out the combined weight of 5 such particles.
2. Multiply the Weight by the Number of Particles:
[tex]\[
\text{Total weight} = (\text{Weight of one particle}) \times (\text{Number of particles})
\][/tex]
[tex]\[
\text{Total weight} = 7.42 \times 10^{-10} \times 5
\][/tex]
3. Perform the Multiplication:
[tex]\[
7.42 \times 5 = 37.1
\][/tex]
4. Calculate the Total Weight Using Scientific Notation:
[tex]\[
\text{Total weight} = 37.1 \times 10^{-10}
\][/tex]
5. Adjust the Scientific Notation:
Since [tex]\(37.1\)[/tex] can be written as [tex]\(3.71 \times 10^1\)[/tex], you can adjust the powers of 10:
[tex]\[
37.1 \times 10^{-10} = 3.71 \times 10^{1} \times 10^{-10} = 3.71 \times 10^{-9}
\][/tex]
Therefore, the total weight of 5 dust particles is [tex]\(3.71 \times 10^{-9}\)[/tex] kilograms. Based on the provided choices, this matches:
- B. [tex]\(3.71 \times 10^{-9}\)[/tex] kilograms
So, the answer is B.
1. Understand the Problem: You have one dust particle weighing [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms, and you need to find out the combined weight of 5 such particles.
2. Multiply the Weight by the Number of Particles:
[tex]\[
\text{Total weight} = (\text{Weight of one particle}) \times (\text{Number of particles})
\][/tex]
[tex]\[
\text{Total weight} = 7.42 \times 10^{-10} \times 5
\][/tex]
3. Perform the Multiplication:
[tex]\[
7.42 \times 5 = 37.1
\][/tex]
4. Calculate the Total Weight Using Scientific Notation:
[tex]\[
\text{Total weight} = 37.1 \times 10^{-10}
\][/tex]
5. Adjust the Scientific Notation:
Since [tex]\(37.1\)[/tex] can be written as [tex]\(3.71 \times 10^1\)[/tex], you can adjust the powers of 10:
[tex]\[
37.1 \times 10^{-10} = 3.71 \times 10^{1} \times 10^{-10} = 3.71 \times 10^{-9}
\][/tex]
Therefore, the total weight of 5 dust particles is [tex]\(3.71 \times 10^{-9}\)[/tex] kilograms. Based on the provided choices, this matches:
- B. [tex]\(3.71 \times 10^{-9}\)[/tex] kilograms
So, the answer is B.
