A real number is any value that represents a quantity along a continuous line, including all rational and irrational numbers. Rational numbers are those that can be expressed as a fraction of two integers, such as 1/2 or -3, while irrational numbers cannot be written as simple fractions—for example, √2 or π. Real numbers include positive numbers, negative numbers, and zero. They are used in everyday measurements such as distance, time, temperature, and many scientific and engineering calculations. Real numbers can be visualized on the number line, which extends infinitely in both directions. The set of real numbers is denoted by the symbol ℝ. Real numbers are essential in mathematics because they form the basis of calculus and real analysis. They follow basic arithmetic operations and properties such as closure, associativity, and distributivity. Understanding real numbers is fundamental to grasping more advanced mathematical concepts. 

Real numbers follow basic arithmetic operations—addition, subtraction, multiplication, and division—and obey algebraic properties such as the distributive, associative, and commutative laws.