## Exercise 1 D

#### Question 1

**Find a rational number between a and b, if**

**(i) **

Sol :

**(ii) **

Sol :

**(iii) **

Sol :

**(iv) **

Sol :

#### Question 2

**Find the two rational numbers between -2 and 2 .**

Sol :

Two rational numbers are 0 , 1

#### Question 3

**Find the three rational numbers between **

Sol :

Let q_{1} , q_{2} and q_{3} are three required rational numbers

q_{1}=

=

=

=

q_{2}=

=

=

=

q_{3}=

=

=

=

#### Question 4

**Find four rational numbers between -1 and .**

Sol :

Let q_{1} , q_{2} , q_{3} and q_{4} are four required rational numbers

q_{1}=

=

=

=

q_{2}=

L.C.M of 4 and 2 is 4

=

=

=

q_{3}=

L.C.M of 8 and 2 is 8

=

=

=

q_{4}=

L.C.M of 16 and 2 is 16

=

=

=

#### Question 5

**Find six rational numbers between -1 and 0**

Sol :

Let q_{1} , q_{2} , q_{3} , q_{4} , q_{5} and q_{6} are six required rational numbers

q_{1}=

=

q_{2}=

=

=

q_{3}=

=

=

q_{4}=

=

=

q_{5}=

=

=

q_{6}=

=

=

#### Question 6

**Insert 10 rational numbers between .**

Sol :

Taking equivalent rationals for

So , 10 rational numbers are ,

#### Question 7

**Insert 100 rational numbers between .**

Sol :

Taking equivalent rationals and

So , ten rational numbers are

#### Question 8

**Find** (i) Six (ii) Sixty

(iii) Six hundred rational numbers between

Sol :

(i)

six rational numbers are

(ii)

Taking equivalent rationals and

Sixty rational numbers are

(iii)

Taking equivalent rationals and

Six hundred rational numbers are