{"id":838250,"date":"2024-07-27T09:36:43","date_gmt":"2024-07-27T04:06:43","guid":{"rendered":"https:\/\/leverageedu.com\/discover\/?p=838250"},"modified":"2024-07-27T09:36:43","modified_gmt":"2024-07-27T04:06:43","slug":"exam-prep-real-numbers","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-real-numbers\/","title":{"rendered":"Real Numbers: Definition,Properties and Examples"},"content":{"rendered":"\n

Real Numbers include both rational and irrational numbers like fractions, integers, and more. The real numbers can be easily represented on a number line with zero in the middle, positive numbers on the right side, and negative numbers on the left side. However, not all the numbers are part of the rational numbers. There are some numbers like \u221a-1, 2 + 3i, and -i, which are not included in the real numbers.A good knowledge of the real numbers is important for various\u00a0competitive exams<\/strong><\/a>\u00a0like\u00a0JEE<\/strong><\/a>,\u00a0NEET<\/strong>,\u00a0SSC<\/strong><\/a>,\u00a0Banking<\/strong><\/a>, and many\u00a0state-level exams<\/strong><\/a>. To better understand this basic idea of the real numbers , let\u2019s go into more detail.<\/p>\n\n\n\n\n\n\n

Definition of Real Numbers<\/h2>\n\n\n\n

Real numbers include all the numbers you can think of that are used in our everyday life. They include whole numbers like 1, 2, 3, and so on, as well as numbers with decimals like 3.14 (which you might know as pi). Even numbers like -5 (negative five) are real numbers. It includes positive and negative integers, fractions, and irrational numbers. However, there are some numbers as well that are not included in the real numbers like rational nor irrational are non-real numbers, like, \u221a-1, 2 + 3i, and -i. These types of numbers are included in complex numbers.<\/p>\n\n\n\n

Also Read: <\/strong>Basics of Prime Numbers<\/strong><\/a><\/p>\n\n\n\n

Set of Real Numbers<\/h2>\n\n\n\n

The set of real numbers, denoted by R, includes all rational and irrational numbers. This includes a wide collection of numbers, including natural numbers (N), whole numbers (W), integers (Z), and rational and irrational numbers. The table below represents the numbers that come under the set of real numbers.<\/p>\n\n\n\n

Number set<\/strong><\/td>Is it a part of the set of real numbers?<\/strong><\/td><\/tr>
Natural Numbers<\/td>Yes<\/td><\/tr>
Whole Numbers<\/td>Yes<\/td><\/tr>
Integers<\/td>Yes<\/td><\/tr>
Rational Numbers<\/td>Yes<\/td><\/tr>
Irrational Numbers<\/td>Yes<\/td><\/tr>
Complex Numbers<\/td>No<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Also Read: <\/strong>Properties of Isosceles Triangle<\/strong><\/a><\/p>\n\n\n\n

Types of Real Numbers<\/h2>\n\n\n\n

All numbers are either rational or irrational. There’s no number that is both or neither. This means every single number you can think of belongs into one of these two groups.<\/p>\n\n\n\n

Rational numbers:<\/strong> These are numbers that can be written as a simple fraction. This includes whole numbers (like 1, 2, 3), fractions (like 1\/2, 3\/4), and decimals that either end (like 0.25) or repeat (like 0.333…).<\/p>\n\n\n\n

Irrational numbers:<\/strong> These are numbers that can’t be written as a simple fraction. They have decimal parts that go on forever without repeating. Famous examples are numbers like pi (3.14159…) and the square root of 2 (1.41421…).<\/p>\n\n\n\n

Symbols of Real Numbers<\/h2>\n\n\n\n

There are certain symbols that we use to represent real numbers and the terms related to them. You can have a look at these symbols below.<\/p>\n\n\n\n