RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev

Mathematics (Maths) Class 9

Class 9 : RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev

The document RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev is a part of the Class 9 Course Mathematics (Maths) Class 9.
All you need of Class 9 at this link: Class 9

RD Sharma Solutions: Exercise 1.1 - Number System


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?

Proof: Yes, zero is a rational number because it is either terminating or non-terminating so we can write in the form of p/q, where p and q are natural numbers and q is not equal to zero. 

So,

p = 0,q = 1,2,3...

Therefore,

RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev


Q.2. Find five rational numbers between 1 and 2.

Proof: We need to find 5 rational numbers between 1 and 2.

Consider,

RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev

And

RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev

So, five rational numbers between 6/6 and 12/6  will be 7/6, 8/6, 9/6, 10/6, 11/6.

Hence 5 rational numbers between 1 and 2 are: RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRevOR RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev


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

Proof: We need to find 6 rational numbers between 3 and 4.

Consider,

RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev

And,

RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev

So, six rational numbers between 21/7 and 28/7 will be RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev

Hence 6 rational numbers between 3 and 4 are RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev


Q.4. Find five rational numbers between RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev and RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev

Proof: We need to find 5 rational numbers between RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev and RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev 

Since, LCM of denominators= LCM (5,5) = 5

So, consider

RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev

And,

RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev

Hence 5 rational numbers between RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev and RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev are: RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev OR RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev


Q.5. Are the following statements true or false? Give reasons 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.

Proof: (i) False, because whole numbers start from zero and natural numbers start from one

(ii) True, because it can be written in the form of a fraction with denominator 1

(iii) False, rational numbers are represented in the form of fractions. Integers can be represented in the form of fractions but all fractions are not integers. for example: RD Sharma Solutions: Number System- 1 Class 9 Notes | EduRev is a rational number but not an integer.

(iv) True, because natural numbers belong to whole numbers

(v) False, because set of whole numbers contains only zero and set of positive integers, whereas set of integers is the collection of zero and all positive and negative integers.

(vi) False, because rational numbers include fractions but set of whole number does not include fractions

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