NCERT Solutions Class 9th Maths Chapter – 1 Number System Exercise – 1.1

Question 1. Is zero a rational number? Can you write this as  p/q , where p and q are integers and q is 0?

Solution – Yes, zero is a rational number which can be written in the form p/q.
0 = 0/1  = 0/2  = 0/3  etc. The denominator q can also be taken as a negative integer.

Question 2. Find the six rational numbers between 3 and 4.

Solution – There are infinite rational numbers between 3 and 4.
we will multiply both the numbers, 3 and 4, with 6 + 1 = 7
i.e., 3 × (7/7) = 21/7
and, 4 × (7/7) = 28/7. 
The numbers in between 21/7 and 28/7 will be rational and will fall between 3 and 4.
Hence, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7 are the 6 rational numbers between 3 and 4.

Question 3. Find five rational numbers between 3/5 and 4/5 .

Solution – There are infinite rational numbers between 3/5 and 4/5.
we will multiply both the numbers 3/5 and 4/5
with 5 + 1 = 6
i.e., (3/5) × (6/6) = 18/30
and, (4/5) × (6/6) = 24/30
The numbers in between 18/30 and 24/30 will be rational and will fall between 3/5 and 4/5.
Hence, 19/30, 20/30, 21/30, 22/30, 23/30 are the 5 rational numbers between 3/5 and 4/5.

Question 4. State whether the following statements are true or false. Give reasons for your answers.

(i) Every natural number is a whole number.

Solution – True
The collection of all natural numbers and 0’s are called whole numbers.

(ii) Every integer is a whole number.

Solution – False
Negative integers are not whole numbers.

(iii) Every rational number is a whole number.

Solution – False
Rational numbers p/q are of the form q 0 and q does not exactly divide p which are not whole numbers.