A number that exists but is not rational is called what?

A number that exists but is not rational is called what?

• A. Irrational Number
• B. Rational Number
• C. Real Number
• D. Prime Number

Answer: (A)

Think of numbers that cannot be written as a ratio of two integers. Such numbers are irrational: they cannot be expressed as p/q with integers p and q (q ≠ 0), and their decimal expansions go on forever without repeating. This fits the description of “exists but is not rational.” Examples include sqrt(2) and pi. Rational numbers can be written as a fraction of integers, so they do fit the opposite property. Real numbers include both rational and irrational numbers, so not all real numbers are irrational. Prime numbers are specific integers and are rational because every integer is rational in the sense of being a fraction b/1 or a/1; they still do not define the broader class of numbers that aren’t rational.

Think of numbers that cannot be written as a ratio of two integers. Such numbers are irrational: they cannot be expressed as p/q with integers p and q (q ≠ 0), and their decimal expansions go on forever without repeating. This fits the description of “exists but is not rational.” Examples include sqrt(2) and pi.

Rational numbers can be written as a fraction of integers, so they do fit the opposite property. Real numbers include both rational and irrational numbers, so not all real numbers are irrational. Prime numbers are specific integers and are rational because every integer is rational in the sense of being a fraction b/1 or a/1; they still do not define the broader class of numbers that aren’t rational.