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Answer :
To solve the problem of finding 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 what the numbers mean:
- A single dust particle weighs [tex]$7.42 \times 10^{-10}$[/tex] kilograms.
- There are [tex]$5 \times 10^6$[/tex] dust particles.
2. Set up the multiplication:
Multiply the weight of one dust particle by the total number of particles to find the total weight:
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
3. Multiply the coefficients and add the exponents:
- Multiply the numerical parts: [tex]\(7.42 \times 5 = 37.1\)[/tex].
- Add the exponents of 10: [tex]\((-10) + (6) = -4\)[/tex].
So, the total weight calculation becomes:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
4. Express in scientific notation:
The expression [tex]\(37.1 \times 10^{-4}\)[/tex] can also be written in scientific notation. To do this, you may adjust it to:
[tex]\[
3.71 \times 10^{-3}
\][/tex]
Therefore, the weight of the [tex]$5 \times 10^6$[/tex] dust particles is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
The correct answer is B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
1. Understand what the numbers mean:
- A single dust particle weighs [tex]$7.42 \times 10^{-10}$[/tex] kilograms.
- There are [tex]$5 \times 10^6$[/tex] dust particles.
2. Set up the multiplication:
Multiply the weight of one dust particle by the total number of particles to find the total weight:
[tex]\[
\text{Total weight} = (7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
3. Multiply the coefficients and add the exponents:
- Multiply the numerical parts: [tex]\(7.42 \times 5 = 37.1\)[/tex].
- Add the exponents of 10: [tex]\((-10) + (6) = -4\)[/tex].
So, the total weight calculation becomes:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
4. Express in scientific notation:
The expression [tex]\(37.1 \times 10^{-4}\)[/tex] can also be written in scientific notation. To do this, you may adjust it to:
[tex]\[
3.71 \times 10^{-3}
\][/tex]
Therefore, the weight of the [tex]$5 \times 10^6$[/tex] dust particles is [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
The correct answer is B. [tex]\(3.71 \times 10^{-3}\)[/tex] kilograms.
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