Any number that can be found in the real world is a **real number(R)**. We find numbers everywhere around us. Natural numbers are used for counting objects, rational numbers are used for representing fractions, irrational numbers are used for calculating the square root of a number, integers for measuring temperature, and so on.

**Types of Real Numbers:**

Different types along with real numbers examples are as given below:

**Natural Numbers(N):**Natural numbers are the counting numbers from 1. For example, they are (1,2,3,4,5,…∞) Natural numbers are a subset of real numbers. It is denoted by N.**Whole Numbers (W):**Numbers (0,1,2,3…∞) are called whole numbers. These are natural numbers, including 0. Whole numbers are also a subset of real numbers. It is denoted by W.**Integers (Z):**The numbers (–∞…, –3,–2,–1,0,1,2,3,4,5, …∞) are called integers. Integers are also a subset of real numbers. It is denoted by Z.**Rational Numbers (Q):**A rational number is defined as a number that can be expressed in the form of p/q, where p and q are co-prime integers and q≠0. Rational numbers are also a subset of real numbers. It is denoted by Q. Examples: (–2/3,0,5,3/10, …. etc).**Irrational Numbers (P):**An irrational number is defined as a number that cannot be expressed in the form of p/q, where p and q are co-prime integers and q≠0. Irrational numbers are also a subset of real numbers. It is denoted by P. Examples: 2–√,5–√,π,e, …. Etc.

Real numbers satisfy the commutative, associative, and distributive laws. These can be stated as :

**Commutative Law of Addition:**

- a + b = b + a

**Commutative Law of Multiplication:**

- a × b = b × a

**Associative Law of Addition:**

- a + (b + c) = (a + b) + c

a + (b + c) = (a + b) + c

**Associative Law of Multiplication:**

- a × (b × c) = (a × b) × c

a × (b × c) = (a × b) × c

**Distributive Law:**

- a × (b + c) = (a × b) + (a × c)

a × (b + c) = (a × b) + (a × c)

or,

(a + b) × c = (a × c) + (b × c)

(a + b) × c = (a × c) + (b × c)

**Real Numbers Examples:**

1

-2/3

3/4

√2

√2 + 5

**Laws of exponents:**

Let a > 0 be a real number and p and q be rational numbers. Then, we have

- a
^{p}.a^{q }= a^{p+q} - a
^{p}/a^{q}= a^{p-q} - (a
^{p})^{q}= a^{pq} - a
^{p}. b^{p}=(ab)^{p}