NCERT Solutions Class 9 Maths Chapter 1 Rational Number Exercise 1.1

 

Introduction:

In this exercise/article we will learn about Rational numbers. A number 'r' is called a rational number, if it can be written in the form \(\displaystyle \frac{p}{q}\) , where p ans q are integers and q ≠ 0. In general, there are infinitely many rational numbers between any two given rational numbers. The rational numbers also include the natural numbers, whole numbers and integers. Now, let us solve some examples about the different types of numbers, which you have studied in earlier classes. 

 

NCERT Class 9 Maths Chapter 1 rational Number :

• NCERT Class 9 Maths Chapter 1 Rational Number Exercise 1.1
• NCERT Class 9 Maths Chapter 1 Rational Number Exercise 1.2
• NCERT Class 9 Maths Chapter 1 Rational Number Exercise 1.3
• NCERT Class 9 Maths Chapter 1 Rational Number Exercise 1.4
• NCERT Class 9 Maths Chapter 1 Rational Number Exercise 1.5

 

Class 9 Maths Exercise 1.1 (Page-05)

Q1. Is zero a rational number? Can you write it in the form \(\displaystyle \frac{p}{q}\), where p and q are intergers and q \(\displaystyle \ne \) 0.

Solution :

Yes, zero is a rational number. It can be written in the form of \(\displaystyle \frac{p}{q}\) but denominator q can also be taken as negative integer [ q \(\displaystyle \ne \) 0 ]. \(\displaystyle \frac{0}{1}\) , \(\displaystyle \frac{0}{2}\) , \(\displaystyle \frac{0}{3}\) etc.

Q2. Find six rational numbers between 3 and 4.

Solution :

There are infinite rational number between 3 and 4.

⇒ 3 × 7 = 21

⇒ 4 × 7 = 28

So, six rational number between 21 to 28 = 22 , 23 , 24 , 25 , 26 , 27

∴ The six rational number between 3 and 4 obtained = 22 , 23 , 24 , 25 , 26 , 27 .

Q3. Find five rational numbers between \(\displaystyle \frac{3}{5}\) and \(\displaystyle \frac{4}{5}\).

Solution :

There are infinite rational number between \(\displaystyle \frac{3}{5}\) and \(\displaystyle \frac{4}{5}\).

⇒ \(\displaystyle \frac{3}{4}\) = \(\displaystyle \frac{3}{5}\,\times \,\frac{6}{6}\) = \(\displaystyle \frac{{18}}{{30}}\)

⇒ \(\displaystyle \frac{4}{5}\) = \(\displaystyle \frac{4}{5}\,\times \,\frac{6}{6}\) = \(\displaystyle \frac{{24}}{{30}}\)

So, five rational number between between \(\displaystyle \frac{{18}}{{30}}\) to \(\displaystyle \frac{{24}}{{30}}\) = \(\displaystyle \frac{{19}}{{30}}\,\) , \(\displaystyle \frac{{20}}{{30}}\,\) , \(\displaystyle \frac{{21}}{{30}}\,\) , \(\displaystyle \frac{{22}}{{30}}\,\) , \(\displaystyle \frac{{23}}{{30}}\,\)

⇒ \(\displaystyle \frac{{19}}{{30}}\,\) , \(\displaystyle \frac{{2}}{{3}}\,\) , \(\displaystyle \frac{{7}}{{10}}\,\) , \(\displaystyle \frac{{22}}{{30}}\,\) , \(\displaystyle \frac{{23}}{{30}}\,\)

∴ The five rational number between \(\displaystyle \frac{3}{5}\) and \(\displaystyle \frac{4}{5}\) obtained = \(\displaystyle \frac{{19}}{{30}}\,\) , \(\displaystyle \frac{{2}}{{3}}\,\) , \(\displaystyle \frac{{7}}{{10}}\,\) , \(\displaystyle \frac{{22}}{{30}}\,\) , \(\displaystyle \frac{{23}}{{30}}\,\).

Q4. State whether the following statements are true or false. Give reasons for your answers.

(i) Every natural number is a whole number.

Solution :

True, because whole number starting 0,1,2,3 ∞ and natural number starting 1,2,3 ∞ that's why every natural number is a whole number.

(ii) Every integers is a whole number.

Solution :

False, because negative integers are not whole number.

(iii) Every rational number is a whole number.

Solution :

False, because rational number is \(\displaystyle \frac{p}{q}\) form but q ≠ 0 and whole number is also \(\displaystyle \frac{p}{q}\) form but q = 0 that's why every rational is not whole number.

 

NCERT Class 9 Maths Chapter 1 rational Number :

• NCERT Class 9 Maths Chapter 1 Rational Number Exercise 1.1
• NCERT Class 9 Maths Chapter 1 Rational Number Exercise 1.2
• NCERT Class 9 Maths Chapter 1 Rational Number Exercise 1.3
• NCERT Class 9 Maths Chapter 1 Rational Number Exercise 1.4
• NCERT Class 9 Maths Chapter 1 Rational Number Exercise 1.5