Mathematics – Class 9 – Chapter 1- Number Systems – Exercise 1.1 – NCERT Exercise Solution

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:

According to the definition of rational number We know that, a number is said to be rational if it can be written in the form p/q , where p and q are integers and q ≠ 0.

Now, according to given question:

Taking the case of ‘0’,

We can write Zero in the form 0/1, 0/2, 0/3 and so on.

We can conclude that 0 can be written in the p/q form, where denominator q can either be positive or negative number.

Hence, 0 is a rational number.

2. Find six rational numbers between 3 and 4.

Solution:

We have to find 6 rational numbers between 3 and 4

Now,

We will multiply 3 and 4, with 6+1 = 7 (any number greater than 6)

So, 3 × (7/7) = 21/7

and, 4 × (7/7) = 28/7.

So, the numbers in between 21/7 and 28/7 will be rational and also will fall between 3 and 4.

Hence, required rational numbers between 3 and 4: 22/7, 23/7, 24/7, 25/7, 26/7, and 27/7.

3. Find five rational numbers between 3/5 and 4/5.

Solution:

We have to find five rational number between 3/5 and 4/5

We will multiply 3/5 and 4/5 with 5+1=6 (any number greater than 5)

So, (3/5) × (6/6) = 18/30

and, (4/5) × (6/6) = 24/30

So, the numbers in between18/30 and 24/30 will be rational and also will fall between 3/5 and 4/5. Hence the required rational number between 3/5 and 4/5: 19/30, 20/30, 21/30, 22/30, and 23/30

4. State whether the following statements are true or false. Give reasons for your answers.

(i) Every natural number is a whole number.

Solution:

True

Reason:

The collection of all natural number (starts from 1, 2, 3 ….) and zero is called whole number (0. 1, 2, …..).

Every natural number is a whole number; but, every whole number is not a natural number because natural number starts from 1 and whole number starts from 0.

(ii) Every integer is a whole number.

Solution:

False

Reason:

From definition, Integers are set of numbers that contain positive, negative and 0; excluding fractional and decimal numbers.

Example: integers= {…-4,-3,-2,-1,0,1,2,3,4…}

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)

Hence, we can say that negative integer number is not whole number.

So, every integer is not whole number.

(iii) Every rational number is a whole number.

Solution:

False

Reason:

From definition,

Rational numbers- All numbers in the form p/q, where p and q are integers and q≠0.

i.e., Rational numbers = 0, 2/3, 5/6 …….

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals). 0, 1, 2,………..

Rational numbers are of the form p/q, q ≠ 0 and q does not divide p completely, that are not whole numbers.

Hence, every whole numbers are rational, but, every rational numbers are not whole numbers.

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