What is a Real Number?

A real number is any value that represents a quantity along a continuous number line. Real numbers include:

• Rational numbers : Numbers that can be expressed as a fraction of two integers (e.g., 1/2, -3, 4.75).
• Irrational numbers : Numbers that cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal expansions (e.g., √2, π, e).

Key Characteristics of Real Numbers:

• They include all positive and negative numbers, zero, fractions, and decimals.
• They can be plotted on a number line.
• Real numbers do not include imaginary or complex numbers (which involve the square root of negative one).

Examples of Real Numbers:

• 7 (integer)
• -3.5 (negative decimal)
• 0 (zero)
• π (irrational)
• 2/3 (rational fraction)

In summary, real numbers are the set of all numbers that you commonly use in everyday counting, measuring, and calculations, forming the foundation of most mathematical concepts.