# Number System – Exercise 1.1 – Class IX

1. Is zero a rational number? can you write it in the form p/q, where p and q are integers and q≠0. ?

Solution:

Yes, zero is rational number. It can be written as 0/1, 0/2 etc., it is in the form of p/q, where p and q are integers and q≠0

1. Find six rational number between 3 and 4

Solution:

To find six rational numbers between 3 and 4 denominator should be made equal to 6+1 = 7

Therefore, 3 = 3×7/7 = 21/7 and 4 = 4×7/7

The six rational numbers between 3 and 4 can be found by varying the numerator between 21 and 28 [because when 28/7 = 4 ]

The numbers are 22/7, 23/7, 24/7, 25/7, 26/7, 27/7.

Solution:

To find five rational numbers between 3/5 and 4/5. Therefore, five rational numbers between 3/5 and 4/5 are 7/10 , 3/4  ,31/40, 63/80, 127/160

1. State whether the following statements are true or false. Give reasons for your answer

(i) Every natural number is a whole number

(ii)Every integer is a whole number

(iii) Every rational number is a whole number

Solution:

(i)True.

The collection of whole numbers contains all the natural numbers.

(ii) False

Negative numbers are not whole numbers.

(iii)False

Rational numbers are of the form p/q , where p and q are integers and q ≠ 0. Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5, … (and so on).