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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 :

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

1. a^p .a^q   = a^p+q
2. a^p/a^q = a^p-q
3. (a^p)^q = a^pq
4. a^p. b^p =(ab)^p