Problem 43 - Introductory and Intermediate Algebra for College Students 4th

Question

Give an example of a number that is an irrational number and a real number.

Step-by-Step Solution

Answer

An example of a number that is both an irrational number and a real number is \(\pi\).

Step 1: Understand Definitions

Know that rational numbers are numbers that can be expressed as a ratio or fraction, whereas irrational numbers can't be expressed as a simple fraction. And real numbers include both rational and irrational numbers.

Step 2: Identify an Irrational Number

Recall that an irrational number's decimal goes on forever without repeating. A well-known example of this is the number \(\pi\), which begins with 3.14 and continues indefinitely without a repeating pattern.

Step 3: Confirm it is a Real Number

Confirm that this chosen number is indeed a real number. Since real numbers include both rational and irrational numbers, and \(\pi\) is an irrational number, it is therefore a real number.