Final answer:
To determine if a number is rational or irrational, we assess if it can be expressed as a fraction. Rational numbers include integers and decimals that terminate or repeat, while irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimals. The term 'rational basis test' refers to a legal standard for assessing certain types of discrimination, not directly linked to numbers.
Step-by-step explanation:
To determine whether each number is rational or irrational, we need to understand the definitions of both terms. A rational number is a number that can be expressed as the quotient or fraction ⅟ of two integers, where a is the numerator and b is the non-zero denominator. An irrational number cannot be expressed as a simple fraction; it's a number that does not repeat and does not end, and it cannot be exactly expressed as a fraction of two integers. Some common examples of irrational numbers are the square root of a non-square number, π (pi), and e (Euler's number). On the other hand, integers, finite decimals, and repeating decimals are all examples of rational numbers. For the numbers that were labelled A) Rational, C) Rational, and D) Rational, we would assume they can be expressed as fractions. For B) Irrational, this number must be one that cannot be written as a fraction. Examples of this decision-making process include: In terms of a law that treats men differently from women, it may indeed be subject to the rational basis test in the context of discrimination. This test determines whether there's a legitimate government interest behind the differing treatment and whether the law is rationally related to that interest.