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.

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

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

Some common examples of irrational numbers are:

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

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

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

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Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to solve problems in other areas of mathematics, such as number and measurement.