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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.

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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.

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