Question

what is an irrational number?

Answer 1

Of the following numbers, which is an integer but does not belong in either of the subsets of integers: −13
, 0, or 13?

Answer 2

An irrational number is a type of real number that cannot be expressed as a simple fraction or quotient of two integers. In other words, if a number cannot be written in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \), it is considered irrational.

Irrational numbers have decimal expansions that are non-terminating and non-repeating. This means that their decimal representations go on forever without forming a repeating pattern. Common examples of irrational numbers include:

- \( \pi \) (pi), which is the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159...
- \( e \) (Euler's number), which is approximately equal to 2.71828...
- The square root of any prime number, such as \( \sqrt{2} \), which is approximately 1.41421...
- The golden ratio, represented by the Greek letter \( \phi \), which is approximately equal to 1.61803...

Irrational numbers are an important part of the number system and play a significant role in various fields of mathematics and science.