3. The repeating decimal 0.111... is equivalent to
Answer: B
0.111... is equivalent to 1/9.
The repeating decimal 0.111... can be expressed as the fraction 1/9. This equivalence arises from the fact that 0.111... represents an infinite series that sums to this fraction.
A) 1/7
The fraction 1/7 equals approximately 0.142857..., which is not equivalent to the repeating decimal 0.111.... Therefore, this option is incorrect.
B) 1/9
The fraction 1/9 is equal to the repeating decimal 0.111..., as it can be derived from the geometric series representation. This makes this option the correct choice.
C) 1/10
The fraction 1/10 is equivalent to 0.1, which does not match the repeating decimal 0.111.... Thus, this option is also incorrect.
D) 1/11
The fraction 1/11 equals approximately 0.090909..., which does not correspond to the repeating decimal 0.111.... Therefore, this option is incorrect as well.
Conclusion
The correct answer is 1/9 because it accurately represents the repeating decimal 0.111.... The other options do not match the value of this decimal, confirming that they are incorrect. Thus, 1/9 is the only suitable equivalent for 0.111....