NCERT solutions for class 9 Maths
Number Systems
Chapter 1
Exercise 1.1
EX 1.1 QUESTION 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 a rational number. It can be written in the form of p/q, q ≠ 0.
Example – 0/1, 0/2, 0/3.
EX 1.1 QUESTION 2.
Find six rational numbers between 3 and 4.
Solution:
To get 6 rational numbers between 3 and 4, the denominator must be 6 + 1 = 7
i.e., 3 × (7/7) = 21/7 and, 4 × (7/7) = 27/7.
Thus, the six rational numbers between 3 and 4 = 22/7, 23/7, 24/7, 25/7, 26/7, 27/7.
Another Method –
Six rational numbers between 3 and 4 = 3.1 , 3.2 , 3.3 , 3.4 , 3.5 , 3.6 .
EX 1.1 QUESTION 3.
Find five rational numbers between 3/5 and 4/5.
Solution:
To get 6 rational numbers between 3/5 and 4/5, the denominator must be 5 + 1 = 6
i.e., (3/5) × (6/6) = 18/30 and, (4/5) × (6/6) = 24/30
Thus, the five rational numbers between 3/5 and 4/5 = 19/30, 20/30, 21/30, 22/30, 23/30.
Another Method –
Six rational numbers between 3/5 and 4/5
convert these numbers into decimals =
3/5 = 0.6 and 4 /5 = 0.8
EX 1.1 QUESTION 4.
State whether the following statements are true or false. Give reasons for your answers.
(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, because the collection of all-natural numbers and 0 is whole numbers.
(ii) False, because negative integers are not whole numbers.
(iii) False, rational numbers are of the form p/q, q ≠ 0. for example – 22/7, 23/7, 24/7, 25/7 etc.
