Answer :
To solve this problem, we need to find the total weight of 5 x 10^6 dust particles, each weighing 7.42 x 10^-10 kilograms, and express it in scientific notation.
### Step-by-Step Solution:
1. Identify the weight of one dust particle:
- We know each dust particle weighs 7.42 x 10^-10 kilograms.
2. Determine the number of dust particles:
- There are 5 x 10^6 dust particles.
3. Calculate the total weight:
- To find the total weight, multiply the weight of one particle by the number of particles.
- Total weight = (7.42 x 10^-10 kilograms) x (5 x 10^6)
4. Perform the multiplication:
- First, multiply the numeric parts: 7.42 x 5 = 37.1
- Then, multiply the powers of ten: 10^-10 x 10^6 = 10^(-10 + 6) = 10^-4
5. Combine the results:
- Total weight = 37.1 x 10^-4 kilograms
6. Express the total weight in proper scientific notation:
- 37.1 x 10^-4 can be written as 3.71 x 10^-3
Therefore, the weight of 5 x 10^6 dust particles is 3.71 x 10^-3 kilograms.
So, the correct answer is B. 3.71 x 10^-3 kilograms.
### Step-by-Step Solution:
1. Identify the weight of one dust particle:
- We know each dust particle weighs 7.42 x 10^-10 kilograms.
2. Determine the number of dust particles:
- There are 5 x 10^6 dust particles.
3. Calculate the total weight:
- To find the total weight, multiply the weight of one particle by the number of particles.
- Total weight = (7.42 x 10^-10 kilograms) x (5 x 10^6)
4. Perform the multiplication:
- First, multiply the numeric parts: 7.42 x 5 = 37.1
- Then, multiply the powers of ten: 10^-10 x 10^6 = 10^(-10 + 6) = 10^-4
5. Combine the results:
- Total weight = 37.1 x 10^-4 kilograms
6. Express the total weight in proper scientific notation:
- 37.1 x 10^-4 can be written as 3.71 x 10^-3
Therefore, the weight of 5 x 10^6 dust particles is 3.71 x 10^-3 kilograms.
So, the correct answer is B. 3.71 x 10^-3 kilograms.
