Question 3

0.111... is equivalent to 1/9.

The repeating decimal 0.111... can be expressed as the fraction 1/9. This is derived from the understanding that 0.111... represents an infinite series where each term contributes to the overall value of the fraction.

A) 1/7

1/7 is approximately 0.142857, which does not match the value of 0.111.... Therefore, this option is incorrect as it does not represent the repeating decimal accurately.

B) 1/9

1/9 equals 0.111..., which perfectly matches the repeating decimal given in the question. This option is correct as it accurately represents the value of the repeating decimal.

C) 1/10

1/10 is equal to 0.1, which is a finite decimal and does not correspond with the repeating decimal 0.111.... Thus, this option is incorrect.

D) 1/11

1/11 is approximately 0.090909..., which does not equal 0.111.... Therefore, this option is also incorrect as it does not represent the repeating decimal.

Conclusion

The correct answer is 1/9, as it accurately converts the repeating decimal 0.111... into a fraction. All other options fail to represent the repeating decimal, either being finite decimals or different repeating sequences.