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Answer :
To find the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles, where each particle weighs [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms, we need to multiply the weight of a single dust particle by the number of particles:
1. Single Dust Particle Weight: [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
2. Number of Dust Particles: [tex]\(5 \times 10^6\)[/tex].
3. Total Weight Calculation:
[tex]\[
(7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
To multiply, you multiply the significant figures and add the exponents:
[tex]\[
7.42 \times 5 = 37.1
\][/tex]
[tex]\[
10^{-10} \times 10^6 = 10^{-4}
\][/tex]
Now, combining these:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
4. Expressing in Scientific Notation:
The correct scientific notation expresses the number so that there is only one non-zero digit to the left of the decimal point. We have:
[tex]\[
37.1 \times 10^{-4} = 3.71 \times 10^{-3}
\][/tex]
Therefore, the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles, expressed in scientific notation, is:
[tex]\[
3.71 \times 10^{-3} \text{ kilograms}
\][/tex]
This corresponds to option B.
1. Single Dust Particle Weight: [tex]\(7.42 \times 10^{-10}\)[/tex] kilograms.
2. Number of Dust Particles: [tex]\(5 \times 10^6\)[/tex].
3. Total Weight Calculation:
[tex]\[
(7.42 \times 10^{-10}) \times (5 \times 10^6)
\][/tex]
To multiply, you multiply the significant figures and add the exponents:
[tex]\[
7.42 \times 5 = 37.1
\][/tex]
[tex]\[
10^{-10} \times 10^6 = 10^{-4}
\][/tex]
Now, combining these:
[tex]\[
37.1 \times 10^{-4}
\][/tex]
4. Expressing in Scientific Notation:
The correct scientific notation expresses the number so that there is only one non-zero digit to the left of the decimal point. We have:
[tex]\[
37.1 \times 10^{-4} = 3.71 \times 10^{-3}
\][/tex]
Therefore, the total weight of [tex]\(5 \times 10^6\)[/tex] dust particles, expressed in scientific notation, is:
[tex]\[
3.71 \times 10^{-3} \text{ kilograms}
\][/tex]
This corresponds to option B.
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