Difficulty: Easy

Average Score: 100%

A medium-sized grain of sand can be approximated as a cube with an edge length of 5 * 10 ^ - 4 meters.

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?

Rationale

2 * 10^3 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.

To estimate the number of medium-sized sand grains lined up to equal one meter, we can assume each grain is approximately 0.5 millimeters in diameter. Thus, 1 meter (1000 millimeters) divided by 0.5 millimeters per grain yields about 2000 grains, or 2 * 10^3.

A (2 * 10^3) CORRECT

This choice correctly calculates the number of grains by taking the total length of 1 meter (1000 millimeters) and dividing it by the average diameter of a medium-sized sand grain (0.5 millimeters). Thus, 1000 / 0.5 = 2000, which is equivalent to 2 * 10^3.

B (2 * 10^4) YOUR ANSWER

This option suggests that there are 20,000 grains in 1 meter, which would imply that each grain measures about 0.05 millimeters. This size is unrealistically small for medium-sized sand grains, making this choice incorrect.

C (2 * 10^6) YOUR ANSWER

This choice indicates 2 million grains, which would mean each grain is only 0.0005 millimeters in diameter. Such a size is far too small for any standard sand grain, leading to an inflated estimate of the number of grains.

D (5 * 10^3) YOUR ANSWER

This option suggests 5000 grains, assuming each grain is 0.2 millimeters in diameter. While this size is plausible, it does not accurately reflect the average size of medium-sized sand grains, making this choice incorrect.

E (5 * 10^4) YOUR ANSWER

This choice proposes 50,000 grains, implying each grain would need to be just 0.02 millimeters in diameter. This size is again too small for medium-sized sand grains, rendering this option incorrect.

Conclusion

The calculation for the number of medium-sized sand grains lining up to 1 meter identifies 2 * 10^3 grains as the correct answer. Each incorrect option either miscalculates the average grain size or significantly underestimates the dimensions of typical sand grains. Understanding the relationship between grain size and total length is crucial for making accurate estimations in such contexts.