## Maths units list

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Maths Query > Unit > Arithmetic > Number System

# Types of Number Natural, Whole, Integer, Real Rational

Found in topics: Numbers

## Natural Number

Any number that matches to a number from 1, 2, 3, 4, …. is called a natural number or counting number.

Example

4, 9 , 11, 35, 99, 500 or 9876 are natural numbers.

Natural numbers are used for counting and ordering. On the basis of that they can be further divided into cardinal and ordinal numbers.

### 1. Cardinal numbers

Cardinal numbers are used for counting of objects. For example, there are 7 apples in a box or there are 7 days in a week. In both examples, we are counting objects which are 7.

### 2. Ordinal numbers

Ordinal numbers are used to order the positions of objects or in other words, we can tell the position of an object.

Example

Example 1
Ist position or 2nd position and so on. The example of ordinal numbers is, girls stood Ist in the race.
Example 2
This is the second largest country in the world.

Note

Set of natural numbers is denoted by N.

## Whole Number

Any number that matches to a number from 0, 1, 2, 3, 4, …. is called a Whole Number.

Example

0, 2, 14 , 23, 48, 172, 623 or 1245 are whole numbers.

Note

Set of whole numbers is denoted by W.

## Integers

All natural numbers and negative of natural numbers including zero are called Integers. It includes 0 and all negative numbers and positive natural numbers.

Example

-65, -12, -5, 0, 56, 89 or 354 are Integers.

Also, the negative numbers are additive inverse of positive corresponding numbers.
What are additive inverse? Additive inverse refers to the sum of a positive number and corresponding negative number is equal to 0.

Example

2 is additive inverse of -2.
Because -2 + 2 = 0.

Note

Zero is neither a negative number nor positive number. It is a neutral number.
Set of integers is denoted by Z.

## Rational Numbers

The numbers each of which can be expressed in the form of $\frac{p}{q}$ , where p and q are integers and q is not equal to zero, are called Rational Numbers.
Besides, the rational numbers are also non terminating and repeating numbers.

Example

$\frac{2}{5}$ , $\frac{1}{3}$ , $\frac{8}{9}$ , $\frac{3}{10}$ etc.

Note

Set of rational numbers is denoted by Q.
Rational number is also a real number.

## Irrational Numbers

The numbers which are not rational are called irrational numbers. Besides, irrational numbers are also non terminating and non repeating numbers.

Example

$\sqrt{2}$ , $\sqrt{5}$ etc.

## Real Numbers

Set of rational numbers and irrational numbers is called Real Numbers. In other words, real numbers include all rational and irrational numbers.

Example

$\sqrt{7}$ , $\frac{1}{8}$ , $\frac{3}{10}$ etc.

All real numbers can be represented on a number line which is also called a real line.

Note

Set of real numbers is denoted by R.

### 1) What is the difference between cardinal and ordinal numbers?

Cardinal numbers are used to count the objects whereas ordinal numbers are used to tell the position of an object.

### 2) What is the difference between rational numbers and irrational numbers?

Rational numbers are non terminating repeating numbers whereas irrational numbers are non terminating non repeating numbers.

### 3) Is zero a rational number?

Yes, zero is a rational number because it is written as $\frac{0}{1}$

Help box
natural
1
position
neutral number
integers
real
repeating
irrational
zero
-7

## Worksheet 2

### Multiple choice questions

a) 2

b) 1

c) 0

d) 3

a) 0

b) 1

c) 2

d) 3

a) 1

b) 2

c) 3

d) 0

#### 4) The irrational number is a

a) non terminating number

b) non repeating number

c) non terminating repeating number

d) non terminating non repeating number

#### 5) 0.333..... is a

a) rational number

b) non repeating number

c) non terminating non repeating number

d) irrational number

#### 6) Integers are collection of all

a) positive numbers

b) negative numbers

c) zero

d) all of the above

#### 7) $\sqrt{2}$ is a

a) rational number

b) irrational number

c) negative number

d) neutral number

a) ∞

b) 2

c) 0

d) 1

a) -9

b) 9

c) 0

d) 1

#### 10) $\frac{11}{10}$ is a

a) rational number

b) irrational number

c) repeating number

d) non terminating number

Last updated on: 30-06-2024