What Are Real Numbers?
Real numbers are a fundamental concept in mathematics that include all the numbers that can be found on the number line. This set encompasses a wide variety of numbers used in everyday life and advanced math.
Definition
Real numbers consist of:
- Rational numbers: Numbers that can be expressed as a fraction ab\frac{a}{b}ba, where aaa and bbb are integers and b≠0b\neq 0b=0. Examples: 1/2, -3, 4.75.
- Irrational numbers: Numbers that cannot be expressed as a simple fraction. Their decimal expansions are non-repeating and non-terminating. Examples: π\pi π, 2\sqrt{2}2, eee.
Characteristics
- They include positive numbers , negative numbers , and zero.
- They can be represented on an infinitely long number line.
- They are used for measuring continuous quantities like length, temperature, and time.
Examples of Real Numbers
- 7
- -3.5
- 0
- 5\sqrt{5}5
- π≈3.14159\pi \approx 3.14159π≈3.14159
Summary
In short, real numbers are all the numbers you can think of that represent quantities along a continuous line, including both rational and irrational numbers. They are essential in virtually all areas of mathematics and science.
