Question

determine if 0.989889888988889888889… is rational or irrational and give a reason for your answer. answer attempt 1 out of 3 the number 0.989889888988889888889… is because

Explanation:

A rational number can be expressed as a fraction of two integers or has a repeating or terminating decimal expansion. An irrational number has a non - repeating and non - terminating decimal expansion. The number \(0.989889888988889888889\ldots\) has a decimal expansion where the pattern of digits (the number of 8s between 9s is increasing: first one 8, then two 8s, then three 8s, etc.) does not repeat in a cyclic manner. So it is a non - repeating and non - terminating decimal.

Answer:

The number \(0.989889888988889888889\ldots\) is irrational because its decimal expansion is non - repeating and non - terminating.