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Class 9 Mathematics

Number System

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Solution of NCERT Exercise 1.1 (Part 1)

Question – 1- Is zero a rational number? Can you write it in the form of p/q, where p and q are integers and q ≠ 0?

Answer –

We know that, raional number is a number which can be written in the form of p/q, where q is not equal to zero. Thus,

(a) Yes, zero is a rational number, as it can be written in the form of p/q.

(b) Since, 0 (zero) is an integer thus, zero can be written in the form of p/q

Example : 0/1, 0/2, 0/3, etc. where 0 (zero) is an integer.

Question – 2 - Find six rational numbers between 3 and 4.

Answer –

First method to find rational number between two number:

A rational number between two numbers can be found by calculating average of two given numbers.

Thus, six rational numbers between given two numbers i.e. 3 and 4 can be calculated as follows:

(1) First rational number between 3 and 4 can be calculated by finding average between them.

class nine math number system 1

(2) As 7/2 is a rational number between 3 and 4, consequently, rational number between 3 and 7/2 will be one of the rational number between 3 and 4, which can be found by calcuating average between 3 and 7/2

class nine math number system 2
class nine math number system 3

(3) Again as as 7/2 is a rational number between 3 and 4, consequently, rational number between 4 and 7/2 will be the rational number between 3 and 4, which can be found by average between 4 and 7/2

class nine math number system 4
class nine math number system 5

(4) Similarly, rational number between 3 and 13/4 will be the rational number between 3 and 4, since 13/4 is a rational number between 3 and 4. Thus next rational number between 3 and 4 can be found by calculating average between 3 and 13/4

class nine math number system 6
class nine math number system 7

(5) Similarly, rational number between 4 and 13/4 will be the rational number between 3 and 4, which can be found by calculating average between 4 and 13/4

class nine math number system 8
class nine math number system 9

(6) Similarly next rational number between 3 and 4 can be found by calculating average between 3 and 15/4, since 15/4 is a rational number between 3 and 4 which we calculated in the step (3).

class nine math number system 10
class nine math number system 11

Thus, six rational numbers between 3 and 4 are 7/2, 13/4, 15/4, 25/8, 29/8 and 27/8.

One can find as many rational number between given any two numbers by calcuating average as above.

Second method to find rational number between two number:

Step – 1: 3 and 4 can also be written as 3/1 and 4/1

Step -2: Since we have to find six rational numbers between 3 and 4, so multiply the numerator and denominator by 6+1 i.e. 7

This will come as follows:

class nine math number system 12
class nine math number system 13

Step – 3: Now, we have to find six rational numbers between 21/7 and 28/7, so, class nine math number system 14 are the six rational numbers between 3 and 4.