Question

Which statement describes - 1/11 ?

A.
It is an irrational number.
B.
It is a rational number that has a repeating decimal expansion.
C.
It is a rational number that has a terminating decimal expansion.
D.
It is not a rational number because it is negative.

Answer 1

Answer:

B

Explanation:

The rational number is the number which can be written as 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. and the prime factorization of q takes the form , 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. and the prime factorization of q does not take the form , 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 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 , then is a rational number that has a repeating decimal expansion. Option B is true.

Explanation:

Answer 2

B

Explanation:

The rational number is the number which can be written as
`(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.
`(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.
`(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
`(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
`(1)/(11)` is a rational number that has a repeating decimal expansion. Option B is true.