1. The problem asks us to classify given numbers as either rational or irrational. 2. A rational number is any number that can be expressed as a fraction \(\frac{a}{b}\) where \(a\) and \(b\) are integers and \(b \neq 0\). 3. An irrational number cannot be expressed as a simple fraction; its decimal form is non-terminating and non-repeating. 4. Given numbers: - Rational: 3.587 (a terminating decimal), 74.721 (a terminating decimal), \(\frac{5}{2}\) (a fraction), 0 (can be written as \(\frac{0}{1}\)), -11 (an integer, can be written as \(\frac{-11}{1}\)) - Irrational: \(\pi\) (non-terminating, non-repeating decimal), \(\sqrt{8}\) (since 8 is not a perfect square, \(\sqrt{8}\) is irrational), 2.72135... (given with ellipsis indicating non-terminating, non-repeating decimal) 5. Therefore, the classification is: **Rational Numbers:** 3.587, 74.721, \(\frac{5}{2}\), 0, -11 **Irrational Numbers:** \(\pi\), \(\sqrt{8}\), 2.72135...