# NCERT Class 9 Solutions: Number Systems (Chapter 1) Exercise 1.1

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**Q.1** Is zero a rational number? Can you write it in the form where p and q are integers and ?

Solution:

Yes, zero is a rational number.

A rational number is a real number that can be written as a simple fraction.

In a fraction both the numerator and denominator are whole numbers.

Most numbers we use in everyday life are Rational Numbers.

Every whole numbers is a rational numbers, because any whole number can be written as a fraction.

For example It can write as etc

Itβs all are form of , where p and q are integers and

**Q.2** Find six rational numbers between 3 and 4

Solution:

Given 2 rational numbers are 3 and 4

To find six rational numbers between 3 and 4

Denominator should be made equal to

So multiply in numerator and denominator by 7 we get,

,

Six rational numbers between 3 and 4 can be found by varying the numerator between 21 and 28

We know that

So, the numbers are

Hence, six rational number between are:

**Q.3** Find five rational numbers between .

Solution:

Given 2 rational numbers are

And to find five rational numbers between

Denominator should be made equal to

So multiply in numerator and denominator by 6 we get,

,

Five rational numbers between can be found by varying the numerator between and

We know that

Therefore, the numbers are

Hence, five rational number between are:

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

Every natural numbers is a whole number.

Every integer is a whole number.

Every rational number is a whole number.

Solution:

1

^{st}statement is True, Since the all whole numbers contains all natural numbers and in additional zero

2

^{nd}statement is false, because Integers include but, Whole numbers include

So, Negatives integers are not whole numbers.

3

^{rd}statement is false, because Rational numbers include but, Whole numbers include

Therefore, numbers are rational number but not whole numbers.