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Answer :
- Multiply the weight of one dust particle by the number of dust particles: $(7.42 \times 10^{-10}) \times (5 \times 10^6)$.
- Multiply the coefficients: $7.42 \times 5 = 37.1$.
- Multiply the powers of 10: $10^{-10} \times 10^6 = 10^{-4}$.
- Express the result in scientific notation: $37.1 \times 10^{-4} = 3.71 \times 10^{-3}$.
- The weight of $5 \times 10^6$ dust particles is $\boxed{3.71 \times 10^{-3}}$ kilograms.
### Explanation
1. Problem Analysis
We are given that a dust particle weighs $7.42 \times 10^{-10}$ kilograms and we want to find the weight of $5 \times 10^6$ dust particles. To do this, we need to multiply the weight of one dust particle by the number of dust particles.
2. Calculating the Total Weight
The total weight is calculated as follows:
$$(7.42 \times 10^{-10}) \times (5 \times 10^6) = (7.42 \times 5) \times (10^{-10} \times 10^6)$$
First, we multiply the coefficients: $7.42 \times 5 = 37.1$.
3. Multiplying Powers of 10
Next, we multiply the powers of 10: $10^{-10} \times 10^6 = 10^{-10+6} = 10^{-4}$.
4. Combining the Results
Combining these results, we get $37.1 \times 10^{-4}$ kilograms. However, to express this in proper scientific notation, the coefficient must be between 1 and 10. So, we rewrite $37.1$ as $3.71 \times 10^1$.
5. Expressing in Scientific Notation
Therefore, the total weight is $(3.71 \times 10^1) \times 10^{-4} = 3.71 \times (10^1 \times 10^{-4}) = 3.71 \times 10^{1-4} = 3.71 \times 10^{-3}$ kilograms.
6. Final Answer
Comparing our result with the given options, we see that the correct answer is B. $3.71 \times 10^{-3}$ kilograms.
### Examples
Scientific notation is extremely useful in fields like astronomy and chemistry, where you often deal with very large or very small numbers. For example, the mass of a planet or the size of an atom are typically expressed in scientific notation to make them easier to handle and compare. This notation simplifies calculations and makes it easier to understand the scale of these quantities.
- Multiply the coefficients: $7.42 \times 5 = 37.1$.
- Multiply the powers of 10: $10^{-10} \times 10^6 = 10^{-4}$.
- Express the result in scientific notation: $37.1 \times 10^{-4} = 3.71 \times 10^{-3}$.
- The weight of $5 \times 10^6$ dust particles is $\boxed{3.71 \times 10^{-3}}$ kilograms.
### Explanation
1. Problem Analysis
We are given that a dust particle weighs $7.42 \times 10^{-10}$ kilograms and we want to find the weight of $5 \times 10^6$ dust particles. To do this, we need to multiply the weight of one dust particle by the number of dust particles.
2. Calculating the Total Weight
The total weight is calculated as follows:
$$(7.42 \times 10^{-10}) \times (5 \times 10^6) = (7.42 \times 5) \times (10^{-10} \times 10^6)$$
First, we multiply the coefficients: $7.42 \times 5 = 37.1$.
3. Multiplying Powers of 10
Next, we multiply the powers of 10: $10^{-10} \times 10^6 = 10^{-10+6} = 10^{-4}$.
4. Combining the Results
Combining these results, we get $37.1 \times 10^{-4}$ kilograms. However, to express this in proper scientific notation, the coefficient must be between 1 and 10. So, we rewrite $37.1$ as $3.71 \times 10^1$.
5. Expressing in Scientific Notation
Therefore, the total weight is $(3.71 \times 10^1) \times 10^{-4} = 3.71 \times (10^1 \times 10^{-4}) = 3.71 \times 10^{1-4} = 3.71 \times 10^{-3}$ kilograms.
6. Final Answer
Comparing our result with the given options, we see that the correct answer is B. $3.71 \times 10^{-3}$ kilograms.
### Examples
Scientific notation is extremely useful in fields like astronomy and chemistry, where you often deal with very large or very small numbers. For example, the mass of a planet or the size of an atom are typically expressed in scientific notation to make them easier to handle and compare. This notation simplifies calculations and makes it easier to understand the scale of these quantities.
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