In the decimal expansion of (0.003)^3 how many zeros are between the decimal point and the first nonzero digit?

Rationale

There are eight zeros between the decimal point and the first nonzero digit in the decimal expansion of (0.003)^3.

To find the decimal expansion of (0.003)^3, we first calculate the value: (0.003)^3 = 0.000000027. In this decimal, there are indeed eight zeros following the decimal point before the first nonzero digit, which is 2.

A (Six) YOUR ANSWER

If there were six zeros, the decimal would read 0.0000002, which is incorrect. The calculation shows that after the decimal point, there are more than six zeros before reaching the first nonzero digit.

B (Seven) YOUR ANSWER

With seven zeros, the decimal would be represented as 0.00000027, which again is not accurate. The actual calculation confirms that there are eight zeros, not seven, before the first nonzero digit.

C (Eight) CORRECT

This choice is correct because, in the decimal expansion 0.000000027, there are exactly eight zeros after the decimal point before the first nonzero digit (2) appears.

D (Nine) YOUR ANSWER

If there were nine zeros, it would imply a decimal like 0.0000000027, which is not the case. The actual value shows that there are only eight zeros before reaching the first nonzero digit.

E (Ten) YOUR ANSWER

Ten zeros would lead to a representation like 0.00000000027, which is incorrect. The calculation shows that the decimal expansion has fewer than ten zeros before the first nonzero digit.

Conclusion

The decimal expansion of (0.003)^3 reveals that there are eight zeros following the decimal point before encountering the first nonzero digit. This understanding is crucial in determining the placement of significant figures and understanding the decimal system in mathematical calculations.

In the decimal expansion of (0.003)^3 how many zeros are between the decimal point and the first nonzero digit?

There are eight zeros between the decimal point and the first nonzero digit in the decimal expansion of (0.003)^3.

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