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.
