10. Which expression best represents the number of medium-sized sand grains that could be lined up side by side to result in a total length of 1 meter?
Answer: A
2 * 10^3
To determine the number of medium-sized sand grains that can be lined up to make a total length of 1 meter, we calculate the number of grains by dividing 1 meter by the edge length of one grain, which is 5 * 10^-4 meters. This calculation yields 2 * 10^3 grains.
A) 2 * 10^3
This option is correct because dividing 1 meter by the length of a single grain (5 * 10^-4 meters) results in 1 / (5 * 10^-4) = 2000, which is equivalent to 2 * 10^3.
B) 2 * 10^4
This option is incorrect because it suggests that there are 20,000 grains of sand. Dividing 1 meter by 5 * 10^-4 meters yields 2,000 grains, not 20,000.
C) 2 * 10^6
This option is also incorrect. It implies there are 2,000,000 grains of sand, which is vastly higher than the actual calculation of 2 * 10^3. The calculations show that this figure does not align with the length of the individual grains.
D) 5 * 10^3
This choice is incorrect as it suggests there are 5,000 grains of sand. The calculation of 1 meter divided by 5 * 10^-4 meters results in 2,000 grains, clearly indicating that this option overestimates the number of grains.
E) 5 * 10^4
This option is incorrect as well. It proposes that there are 50,000 grains, which is not supported by the calculations. The correct number, as derived from the length of the grains, is 2,000 grains.
Conclusion
The correct answer, 2 * 10^3, accurately represents the calculated number of medium-sized sand grains that can line up to make a total length of 1 meter. All other options either overestimate or underestimate this number based on the provided measurements, demonstrating that they do not properly reflect the relationship between the length of the grains and the total desired length.