Complete each sentence to describe irrational numbers. An irrational number can [always / sometimes / never] be written as the quotient of two integers, a/b, where b != 0.
![Complete each sentence to describe irrational numbers. An irrational number can [always / sometimes / never] be written as the quotient of two integers, a/b, where b != 0.](https://media.hwhelper.com/6b173201-e51f-4a32-ad7b-36494cd7612f-compressed.jpg)
Answer
By definition, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, a and b, with the denominator b not equal to zero. An irrational number, on the other hand, is defined as a real number that cannot be expressed as a ratio of integers; its decimal representation is non-terminating and non-repeating. Therefore, an irrational number can never be written as the quotient of two integers. The correct choice to fill in the blank is 'never'.