which of these numbers can be classified as both real and irrational?
To determine which numbers can be classified as both real and irrational, it is important to understand the definitions of these terms:
1. Real numbers: Real numbers include all rational numbers (numbers that can be expressed as fractions) and all irrational numbers (numbers that cannot be expressed as fractions).
2. Irrational numbers: Irrational numbers cannot be expressed as fractions and their decimal representations neither terminate nor repeat. They are non-repeating and non-terminating decimals.
Now, we need to identify numbers that fit both conditions:
1. Real numbers: All numbers are real, including both rational and irrational numbers.
2. Irrational numbers: Examples of irrational numbers include π (pi), √2 (the square root of 2), e (Euler's number), and √3 (the square root of 3). These numbers cannot be expressed as fractions and have non-repeating decimal representations.
Therefore, any number that belongs to the set of irrational numbers is automatically considered both real and irrational. Examples include π, √2, e, and √3.