Answer:
B
Step-by-step explanation:
The rational number is the number which can be written as [tex]\frac{p}{q},[/tex] where q is natural and p is integer.
Theorem: If m is a rational number, which can be represented as the ratio of two integers i.e. [tex]\frac{p}{q},[/tex] and the prime factorization of q takes the form [tex]2^x\cdot 5^y[/tex], where x and y are non-negative integers then, it can be said that m has a decimal expansion which is terminating.
Theorem: If m is a rational number, which can be represented as the ratio of two integers i.e. [tex]\frac{p}{q},[/tex] and the prime factorization of q does not take the form [tex]2^x\cdot 5^y[/tex], where x and y are non-negative integers. Then, it can be said that m has a decimal expansion which is non-terminating repeating (recurring).
The fraction [tex]\frac{1}{11}[/tex] is a rational number, because 1 is integer and 11 ia natural. So, options A and D are false.
Since we cannot represent 11 as a product [tex]2^x\cdot 5^y[/tex], then [tex]\frac{1}{11}[/tex] is a rational number that has a repeating decimal expansion. Option B is true.
