Irrational numbers

Definition

Irrational numbers are real numbers that cannot be expressed as a simple fraction of two integers. They have non-repeating, non-terminating decimal expansions.

5 Must Know Facts For Your Next Test

1. The square root of any non-perfect square is an irrational number.
2. $\pi$ (pi) and $e$ (Euler's number) are classic examples of irrational numbers.
3. Irrational numbers do not have a repeating or terminating decimal representation.
4. The sum or product of a rational number and an irrational number is always irrational.
5. Irrational numbers are part of the real number system but are distinct from rational numbers.

Review Questions

• Explain why $\sqrt{2}$ is an irrational number.
• Can the sum of two irrational numbers be rational? Provide an example to support your answer.
• Is the decimal expansion $3.14159...$ terminating or repeating?

Related terms

Rational Numbers: Numbers that can be expressed as a fraction of two integers, where the denominator is not zero.

Real Numbers: All numbers on the number line, including both rational and irrational numbers.

$\pi$ (Pi): An irrational number representing the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159.