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:

1. 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.
2. 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.
3. 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.
4. 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).
5. 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 :

• a + b = b + a

Commutative Law of Multiplication:

• a × b = b × a

• 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

1. ap .aq   = ap+q
2. ap/aq = ap-q
3. (ap)q = apq
4. ap. bp =(ab)p