Related Articles

# Class 9 RD Sharma Solutions – Chapter 1 Number System – Exercise 1.1

• Last Updated : 27 Nov, 2020

### 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.

Attention reader! All those who say programming isn't for kids, just haven't met the right mentors yet. Join the  Demo Class for First Step to Coding Coursespecifically designed for students of class 8 to 12.

The students will get to learn more about the world of programming in these free classes which will definitely help them in making a wise career choice in the future.

It can be written in p/q form provided that q ≠ 0.

For Example: 0/5, 0/6, 0/7 etc.

### Question 2: Find five rational numbers between 1 and 2.

Solution:

We know how to find a rational number between two numbers x and y = (x + y)/2

Now let’s find 5 rational numbers between 1 and 2.

Step 1: Rational number between 1 and 2

= (1 + 2)/2

= 3/2

Step 2: Rational number between 1 and 3/2

= (1 + 3/2)/2

= 5/4

Step 3: Rational number between 1 and 5/4

= (1 + 5/4)/2

= 9/8

Step 4: Rational number between 3/2 and 2

= 1/2 [(3/2) + 2)]

= 7/4

Step 5: Rational number between 7/4 and 2

= 1/2 [7/4 + 2]

= 15/8

Therefore, 5 rational numbers between 1 and 2 are 9/8, 5/4, 3/2, 7/4, 15/8

### Question 3: Find six rational numbers between 3 and 4.

Solution:

To find n rational numbers between any two rational numbers we have to Multiply and divide both the numbers by n+1.

n = 6

So, n + 1 = 7

Multiplying and dividing 3 and 4 by 7,

3 × 7/7 = 21/7

4 × 7/7 = 28/7

Now we have to choose 6 rational numbers between 21/7 and 28/7

Therefore, 6 rational numbers between 3 and 4 are 22/7, 23/7, 24/7, 25/7, 26/7, 27/7

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

Solution:

To find n rational numbers between any two rational numbers we have to Multiply and divide both the numbers by n+1.

n = 5

So, n + 1 = 6

Multiplying and dividing 3/5 and 4/5 by 6,

3/5 × 6/6 = 18/30

4/5 × 6/6 = 24/30

Now we have to choose 5 rational numbers between 18/30 and 24/30

Therefore, 5 rational numbers between 3/5 and 4/5 are 19/30, 20/30, 21/30, 22,30, 23/30

### Question 5: Are the following statements true or false? Give a reason for your answer.

(i) Every whole number is a natural number.

(ii) Every integer is a rational number.

(iii) Every rational number is an integer.

(iv) Every natural number is a whole number,

(v) Every integer is a whole number.

(vi) Every rational number is a whole number.

Solution:

(i) False.

Reason: because 0 is a whole number but not a natural number.

(ii) True

Reason: because every integer can be represented in the form of a fraction n/1.

(iii) False.

Reason: numbers such as 4/3, 2/9, 7/5 are rational numbers but not integers.

(iv) True.

Reason: every natural number is a whole number because whole numbers are positive integers including 0 and natural number are positive integers.

(v) False.

Reason: Negative numbers are not whole numbers.

(vi) False.

Reason: numbers such as 4/3, 2/9, 7/5 are rational numbers but not whole numbers.

My Personal Notes arrow_drop_up