# Class 9 NCERT Solutions- Chapter 1 Number System – Exercise 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:**

A number is a rational number if it can be written in the form of p/q, where p and q are integers and q ≠ 0

- Therefore, we can write 0 in the form of 0/1, 0/2, 0/3, 0/4.
- As well as, q can be a negative integer also, 0/-1, 0/-2, 0/-3, 0/-4.

So we can see 0 can be written in p/q, form hence 0 is a rational number.

**Question 2: Find six rational numbers between 3 and 4.**

**Solution: **

We can find infinite rational numbers between 3 and 4.

Now we have to find 6 rational numbers between 3 and 4 we will multiply and divide both the numbers 3 and 4 by (6 + 1) 7.

- 3 = 3 × 7/7 = 21/7
- 4 = 4 × 7/7 = 28/7
Hence the 6 rational numbers are 23/7, 24/7, 25/7, 26/7, 27/7, and 28/7.

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

**Solution: **

We need to find 5 rational numbers between 3/5 and 4/5.

Multiply both numerator and denominator by (5 + 1) 6.

- 3/5 = 3/5 × 6/6 = 18/30
- 4/5 = 4/5 × 6/6 = 24/30
Hence, the 5 rational number between 3/5 and 4/5 are 19/30, 20/30, 21/30, 22/30 and 23/30.

**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) Every natural number is a whole number.True

Explanation:The natural numbers starts from 1, 2, 3, 4 …..

The whole number starts from 0, 1, 2, 3 , 4 …..

Here it is clearly seen that whole number contains all the natural numbers and 0 also

Therefore, every natural number is a whole number but not every whole number is not a natural number as 0 is a whole number but not a natural number.

(ii) Every integer is a whole number.False

Explanation:Integers are the numbers that have both positive and negative numbers including 0,Example: …..-4, -3, -2, -1, 0, 1, 2, 3, 4 ……

Whereas whole numbers begin from 0 to infinite

Example: 0, 1, 2, 3, 4…..

Here we can see every whole number is an integer but not all the integers are the whole number.

(iii) Every rational number is a whole number.False

Explanation:Rational numbers are the numbers that can be written in the form of p/q where q ≠ 0.Example: 0, 2/5, 4/17, 7/15 …..

Whole numbers are that starts from 0 to infinity

As we know whole numbers can be written in the form of 0/1, 1/1, 2/1, …Thus, every whole number is a rational number but every rational number is not a whole number.