Question

Which statement describes - 1/11 ?

Answer 1

Answer:

B

Step-by-step explanation:

The rational number is the number which can be written as $\frac{p}{q},$ 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. $\frac{p}{q},$  and the prime factorization of q takes the form $2^x\cdot 5^y$, 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. $\frac{p}{q},$  and the prime factorization of q does not take the form $2^x\cdot 5^y$, 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 $\frac{1}{11}$ 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 $2^x\cdot 5^y$, then $\frac{1}{11}$ is a rational number that has a repeating decimal expansion. Option B is true.