Question

Explain :-

1. Irrational numbers with examples

2. Real numbers with examples

3. Integers with examples

4. Whole numbers with examples

5. Natural numbers with examples​

Answer 1

Irrational number :

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0.

• Example: √2, √3, √5, √11, √21, π(Pi) are all irrational

Real Numbers:

Real numbers are the numbers which include both rational and irrational numbers.

• Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.

Integers:

An integer (from the Latin integer meaning "whole") is colloquially defined as a number that can be written without a fractional component.

• For example, 21, 4, 0, and −2048 are integers, while 9.75, 512, and √2 are not.

Whole number:

In mathematics, whole numbers are the basic counting numbers 0, 1, 2, 3, 4, 5, 6, … and so on. 17, 99, 267, 8107 and 999999999 are examples of whole numbers. Whole numbers include natural numbers that begin from 1 onwards.

• Whole numbers include positive integers along with 0.

Natural number:

A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc. Natural numbers are also called "counting numbers" because they are used for counting.

• For example, if you are timing something in seconds, you would use natural numbers (usually starting with 1).

Answer 2

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Irrational Numbers :

• An irrational number is the real number whose decimal representation is a non terminating, non repeating decimal number.

Example : 0.5252252222...

Real Numbers :

• A real number is any number that can be found on a number line. The rational numbers and irrational numbers combined to form a real number.

Example :7, 0,⅔, √2 etc.

Integers :

• An integer is a whole number (not a fractional number) that can be positive, negative or zero.

Example : -1, -4, -3, 0,1,2 etc.

Whole Numbers :

• The set of all combination of digit is known as whole numbers .

Example : 0,1,2,3..to infinity.

Natural Numbers :

• The numbers that are defined as counting numbers ; positive integers beginning with 1 and increasing by 1 forever is known as natural numbers.

Ex : 1,2,3 to infinity.

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• 0 is not a natural number .

Any number that can be expressed as fraction a/b, where a and b both are integers but b cannot be zero is known as rational numbers.

Example : 2/4,8/2 etc..