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Answer :
To solve this question, we compare the given approximate masses of a grain of sand.
1. Mass of a grain of sand given in scientific notation:
- The first mass is [tex]\(2.8 \times 10^{-11}\)[/tex] grams.
- The second mass is approximately [tex]\(2 \times 10^{-8}\)[/tex] grams.
2. Understanding the numbers:
- [tex]\(2.8 \times 10^{-11}\)[/tex] grams means that the decimal point is moved 11 places to the left from the number 2.8.
- [tex]\(2 \times 10^{-8}\)[/tex] grams means that the decimal point is moved 8 places to the left from the number 2.
3. Comparing the values:
- The mass [tex]\(2.8 \times 10^{-11}\)[/tex] grams is a much smaller number compared to [tex]\(2 \times 10^{-8}\)[/tex] grams. This is because moving the decimal point further to the left results in a smaller value.
4. Conclusion:
- Based on the comparison, [tex]\(2.8 \times 10^{-11}\)[/tex] grams refers to a notably smaller mass than [tex]\(2 \times 10^{-8}\)[/tex] grams. Thus, the grain of sand is significantly lighter with the first approximation.
This step-by-step solution outlines the process of comparing the two masses expressed in scientific notation to determine which value is correct based on the scale of the numbers.
1. Mass of a grain of sand given in scientific notation:
- The first mass is [tex]\(2.8 \times 10^{-11}\)[/tex] grams.
- The second mass is approximately [tex]\(2 \times 10^{-8}\)[/tex] grams.
2. Understanding the numbers:
- [tex]\(2.8 \times 10^{-11}\)[/tex] grams means that the decimal point is moved 11 places to the left from the number 2.8.
- [tex]\(2 \times 10^{-8}\)[/tex] grams means that the decimal point is moved 8 places to the left from the number 2.
3. Comparing the values:
- The mass [tex]\(2.8 \times 10^{-11}\)[/tex] grams is a much smaller number compared to [tex]\(2 \times 10^{-8}\)[/tex] grams. This is because moving the decimal point further to the left results in a smaller value.
4. Conclusion:
- Based on the comparison, [tex]\(2.8 \times 10^{-11}\)[/tex] grams refers to a notably smaller mass than [tex]\(2 \times 10^{-8}\)[/tex] grams. Thus, the grain of sand is significantly lighter with the first approximation.
This step-by-step solution outlines the process of comparing the two masses expressed in scientific notation to determine which value is correct based on the scale of the numbers.
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