A medium-sized grain of sand can be approximated as a cube with an edge length of 5X10Ã¢»Ã¢´ 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

2X10⁴ 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 find the number of sand grains that can fit into 1 meter, divide 1 meter by the edge length of a grain of sand, which is 5 × 10⁻⁴ meters. This calculation results in 2 × 10⁴ grains.

A (2X10³) YOUR ANSWER

This choice represents a value that is 10 times smaller than the correct answer. It would suggest that only 1,000 grains could fit in a meter, which is inaccurate given the size of the grains specified.

B (2X10⁴) CORRECT

This choice accurately reflects the number of sand grains that can fit in a meter after performing the division of 1 meter by the edge length of a sand grain (5 × 10⁻⁴ meters). The result is indeed 2 × 10⁴, confirming this as the correct answer.

C (2X10⁵) YOUR ANSWER

This choice indicates a value that is 10 times larger than the correct answer. It suggests that 200,000 grains could fit within 1 meter, which is incorrect given the size of the grains being considered.

D (5X10³) YOUR ANSWER

This choice suggests that only 5,000 grains can fit into a meter. This is significantly lower than the correct calculation, demonstrating a misunderstanding of the size relationship between the grains and a meter.

E (5X10⁴) YOUR ANSWER

This choice is twice the correct answer. It implies that 50,000 grains could fit in 1 meter, which overestimates the number based on the provided grain size.

Conclusion

The calculation of how many medium-sized grains of sand can fit into 1 meter is essential in various scientific applications. By correctly dividing the length of 1 meter by the size of each grain, we determined that 2 × 10⁴ grains can fit side by side. This understanding of unit conversion and size comparison is fundamental in physical sciences and engineering contexts.