Irrational Numbers

An irrational number is a number that cannot be expressed as a fraction of two integers and its decimal representation goes on forever without repeating. In other words, it cannot be written as a simple fraction.

Characteristics of Irrational Numbers

• Cannot be expressed as a simple fraction
• Have non-repeating, non-terminating decimal representations
• Examples include: √2, π (pi), and e (Euler's number)

Representations of Irrational Numbers

Irrational numbers can be represented in different forms, such as:

1. Root form: √2, √3
2. Decimal form: 3.14159265359...
3. Continued fraction form: [1; 1, 1, 1, 1, ...]

Examples of Irrational Numbers

Some common examples of irrational numbers are:

• √2 ≈ 1.41421356...
• π (pi) ≈ 3.14159265...
• e (Euler's number) ≈ 2.71828183...

Study Tips for Understanding Irrational Numbers

To better understand irrational numbers, consider the following study tips:

1. Practice estimating the values of irrational numbers using their decimal approximations.
2. Explore the concept of square roots and their connection to irrational numbers.
3. Use visual aids, such as number lines and geometric representations, to illustrate irrational numbers.
4. Compare and contrast irrational numbers with rational numbers to understand their differences.