Final answer:
The expression consists of decimals and repeating decimals; rational numbers are expressed as fractions while irrationals cannot. Repeating decimals are rational. The presence of a single irrational number makes the entire expression irrational.
Step-by-step explanation:
The question asks whether the expression given, which consists of several decimal numbers and repeating decimals, is rational or irrational. Rational numbers can be expressed as the quotient of two integers, while irrational numbers cannot be expressed as a simple fraction and have endless non-repeating decimals. To determine the nature of each number given in the expression and thus if the entire expression is rational or irrational, we must analyze them one by one. For example, -0.6 is rational as it can be written as -6/10 or -3/5 after simplification. Numbers with a repeating pattern, such as -0.292929292929..., are also rational, as they can be expressed as fractions. Numbers like pi or e are examples of irrational numbers since they cannot be written as simple fractions and their decimal representations are non-terminating and non-repeating. If the expression contains even one irrational number, the result will be irrational. Otherwise, if all numbers are rational, the resulting expression will also be rational.