Irrational numbers

Definition

Irrational numbers are real numbers that cannot be expressed as a 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 prime number is an irrational number.
2. Pi (π) and Euler's number (e) are well-known examples of irrational numbers.
3. Irrational numbers cannot be precisely represented in decimal or fractional form.
4. The sum or product of a rational number and an irrational number is always irrational.
5. Irrational numbers are dense on the real number line, meaning between any two rational numbers, there exists at least one irrational number.

Review Questions

• What distinguishes an irrational number from a rational number?
• Give an example of an irrational number and explain why it is classified as such.
• Can the sum of two irrational numbers be rational? Explain.

Related terms

Rational Numbers:

Rational numbers can be expressed as the quotient or fraction of two integers where the denominator is not zero.

Real Numbers:

Real numbers include all rational and irrational numbers, encompassing all possible magnitudes along the continuous number line.

Prime Numbers: Prime numbers are natural numbers greater than 1 that have no divisors other than 1 and themselves.