Exercise 1.1 NCERT Solutions: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9

Q1. Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0?

Ans: We know that, a number is said to be rational if it can be written in the form p/q, where p and q are integers and q ≠ 0.
Taking the case of ‘0’,
Zero can be written in the form 0/1, 0/2, 0/3 … as well as, 0/1, 0/2, 0/3 ....
Since it satisfies the necessary condition, we can conclude that 0 can be written in the p/q form, where q can either be positive or negative number.
Hence, 0 is a rational number.

Q2. Find six rational numbers between 3 and 4.

Ans: There are infinite rational numbers between 3 and 4.
As we have to find 6 rational numbers between 3 and 4, we will multiply both the numbers, 3 and 4, with 6 + 1 = 7 (or any number greater than 6)
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.

Q3. Find five rational numbers between 3/5 and 4/5.

Ans: There are infinite rational numbers between 3/5 and 4/5.
To find out 5 rational numbers between 3/5 and 4/5, we will multiply both the numbers 3/5 and 4/5
with 5 + 1 = 6 (or any number greater than 5)
i.e., (3/5) × (6/6) = 18/30
and, (4/5) × (6/6) = 24/30
The numbers in between18/30 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

Q4. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.

Ans: True
Natural numbers- Numbers starting from 1 to infinity (without fractions or decimals)
i.e., Natural numbers= 1,2,3,4…
Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)
i.e., Whole numbers= 0,1,2,3…
Or, we can say that whole numbers have all the elements of natural numbers and zero.
Every natural number is a whole number; however, every whole number is not a natural number.

(ii) Every integer is a whole number.

Ans: False
Integers: Integers are set of numbers that contain positive, negative and 0; excluding fractional and decimal numbers.
i.e., integers = {…-4,-3,-2,-1,0,1,2,3,4…}
Whole numbers: Numbers starting from 0 to infinity (without fractions or decimals)
i.e., Whole numbers = 0,1,2,3….
Hence, we can say that integers include whole numbers as well as negative numbers.
Every whole number is an integer; however, every integer is not a whole number.

(iii) Every rational number is a whole number.

Ans: False
Rational numbers: All numbers in the form p/q, where p and q are integers and q ≠ 0.
i.e., Rational numbers = 0, 19/30 , 2, 9/-3, -12/7…
Whole numbers: Numbers starting from 0 to infinity (without fractions or decimals)
i.e., Whole numbers = 0,1,2,3….
Hence, we can say that integers include whole numbers as well as negative numbers.
Every whole number is rational, however, every rational number is not a whole number.