Question 2

There are eight zeros between the decimal point and the first nonzero digit.

When calculating (0.003)^3, the result is 0.000000027, which shows that there are eight zeros following the decimal point before reaching the first nonzero digit, which is 2.

A) Six

This option is incorrect because the calculation shows there are eight zeros in total, not six. Counting only six would overlook some of the zeros present in the decimal expansion.

B) Seven

This choice is also incorrect. While seven zeros might seem plausible at first glance, a careful evaluation of the decimal expansion reveals that there are in fact eight zeros before the first nonzero digit.

C) Eight

This is the correct answer as the decimal expansion of (0.003)^3 is 0.000000027, which clearly contains eight zeros between the decimal point and the first nonzero digit (2).

D) Nine

This option is incorrect because it suggests there are nine zeros, which exceeds the actual count. The decimal expansion only reveals eight zeros before the first nonzero digit.

E) Ten

This option is incorrect as well. The total number of zeros in the decimal expansion is only eight, making ten an overestimation of the zeros present.

Conclusion

The correct answer is definitively C) Eight, as it accurately reflects the number of zeros in the decimal expansion of (0.003)^3 before the first nonzero digit. All other options miscount the zeros, demonstrating a misunderstanding of the decimal representation resulting from the cubic calculation.