Rational Numbers

Rational numbers are a fundamental concept in mathematics that form the basis of our number system. A rational number can be defined as any number that can be expressed as the ratio of two integers. This means that rational numbers can be written as fractions, where the numerator and denominator are both integers. They include whole numbers, integers, and terminating or repeating decimals. Rational numbers are incredibly versatile and are used in various mathematical operations, including addition, subtraction, multiplication, and division. Understanding rational numbers is essential for solving real-world problems in fields such as finance, engineering, and science.

Practice 1

Practice 2

Irrational Numbers

Irrational numbers are a special type of number that cannot be expressed as a fraction and have an infinite and non-repeating decimal expansion. Examples of irrational numbers include the square root of 2, (√2), and pi (π). These numbers play a crucial role in mathematics, challenging our understanding of numbers and their properties.

Practice 3

Real Numbers

Real numbers are the set of all rational and irrational numbers, forming an infinite continuum on the real number line, which extends infinitely in both positive and negative directions. This number line serves as a visual representation of the order and magnitude of real numbers, showcasing their vastness and interconnectedness.

Practice 4

Sets of Numbers as Subsets

Real number subsets are essential for organizing and categorizing the expansive set of real numbers. For example, the subset of even numbers consists of integers that are divisible by 2, while the subset of rational numbers includes all numbers that can be expressed as a fraction of two integers. These subsets allow mathematicians to study and analyze specific properties and characteristics within the broader realm of real numbers.

Practice 5