**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.