Final answer:
The rational number that lies between 1/9 and 0.7 repeating (7/9) from the given options is 4/9, making option c the correct answer.
Step-by-step explanation:
The question asks which rational number lies between 1/9 and 0.7 (repeating). To find this number, we need to convert the repeating decimal to a fraction. The decimal 0.7 repeating is equal to 7/9 as a fraction. Now we compare the fractions 1/9, 1/13, 1/11, 4/9, and 9/11 to find which is between 1/9 and 7/9.
1/13 is less than 1/9.
1/11 is greater than 1/9 but less than 7/9.
4/9 is greater than 1/9 and also less than 7/9 making it a potential answer.
9/11 is greater than 7/9 and therefore not between 1/9 and 7/9.
Between the options given, both 1/11 and 4/9 are between 1/9 and 7/9, but 4/9 is closer to 7/9 than 1/11. Therefore, the correct answer is c. 4/9.