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

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

Yes, zero is a rational number.
Zero can be written as:
Example : 
Which is in the form of p/q where p and q are integers and q ≠ 0.

Q.2. Find six rational numbers between 3 and 4.

We can find any number of rational numbers between two rational numbers. First of all, we make the denominators same by multiplying or dividing the given rational numbers by a suitable number. If denominator is already same then depending on number of rational no. we need to find in question, we add one and multiply the result by numerator and denominator.

We can choose 6 rational numbers as: and

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

Since we make the denominator same first, then

Now we need to find 5 rational no.

∴ Five rational numbers between areand

Q.4. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.

True, because the set of natural numbers is represented as N= {1, 2, 3…….} and the set of whole numbers is W = {0, 1, 2, 3 ………}. We see that every natural number is present in the set of whole numbers.

(ii) Every integer is a whole number.

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.

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.