An integer is like a whole number (28 is an integer). Irrational means the decimal goes on forever.......and cannot be written as a fraction (0.9857... is irrational). A number that is not real is the squareroot of a negative, or something times i, or dividing by zero (5/0 is unreal). A rational number can be written as a fraction (like 8 and 1/7).
