# Rational and Irrational Numbers | Lesson No.1

Rational and irrational numbers :

First we will see, What are the types of Numbers ?
We are very much familiar with Natural Numbers, Whole Numbers, Integers and Rational Numbers.

Natural Numbers : All positive numbers are called as Natural Numbers.
e.g. : 1,2,3,4,5……

Whole Numbers : All Natural Numbers and zero are called as Whole Numbers.
e.g. : 0,1,2,3,4,5……

Integers Numbers : All positive and Negative numbers including zero are called as Integers.
e.g. : …..-5,-4,-3,-2,-1, 0,1,2,3,4,5……

Rational Numbers : The number in the form of m/n (fraction numbers) are called rational numbers.
Here ‘m’ and ‘n’ are integers, but ‘n’ should not be zero.

 25 , 10 , 57 , 31 , −4, 0, 3, 8, 10 etc. 3 −7 6 4

## Practice Set 1.1

1. Show the following number on a number line. Draw a separate number line for each example.

 (1) 3 , 5 , − 3 2 2 2

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 (2) 7 , −2 , −4 5 5 5

Shown on the number line as follows :

 (3) −5 , 11 8 8
 (4) 13 , − 17 10 10

➤ First check the denominator, here denominator is ‘10’.
Step-I : Draw a line and place numbers on it like -2, -1, 0, 1, 2.
Step-II : Make 10 equal parts of each unit.
Step-II : Show the given rational numbers on the number line.

2. Observe the number line and answer the questions.

(1) Which number is indicated by point B?

 (2) Which point indicates the number 1 3 ? 4
 (3) State whether the statement, ‘the point D denotes the number 5 ‘ is true or false. 2

Ans .
(1) Observe the line figure given above.

• Count the numbers between ‘0’ to ‘1’ : it is 4, it means denominator should be ‘4’.
• Now count the numbers between ‘O’ to ‘B’ : it is 10, it is left side of the zero, so it is ‘−10’.
 So Answer is : The number is indicated by point B is : −10 . 4

(2) Observe the question 1 complete number and there after ‘3’.

• it means this number is indicates the point ‘C’.

(3) Again denominator is ‘4’, count till D is ’10’.

 So the fraction is : 10 = 10 ÷ 2 = 5 4 4 ÷ 2 2

Ans : True.

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