# RD Sharma Class 9 Number System Exercise 1.1 Solutions

On this page you will find Maths RD Sharma Class 9 Number System Exercise 1.1 Solutions. The solutions provided here are to help students practice math problems and get better at solving difficult chapter questions. Maths chapter 1 for class 9 deals with the topic of triangles and it is one of the most important chapters.

## Download RD Sharma Class 9 Number System Exercise 1.1 Solutions in PDF

Students can use these solutions to overcome the fear of maths and the solutions have been designed in such a way that it enables them to discover easy ways to solve different problems. These solutions can help students in refining their maths fluency and problem-solving skills. Students can go through the RD Sharma solutions for class 9 chapter 1 Number System Exercise 1.1 below and it will be beneficial for them.

## RD Sharma Class 9 Number System Exercise 1.1 Solutions

Q1. Is 0 a rational number? Can you write it in the form $\frac{P}{Q}$, where $P$ and $Q$ are integers and $Q \neq 0$ ?
Solution:
Yes, 0 is a rational number and it can be written in $\mathrm{P} \div \mathrm{Q}$ form provided that $\mathrm{Q} \neq 0$
0 is an integer and it can be written various forms, for example
$0 \div 2,0 \div 100,0 \div 95$ etc.

Q2. Find five rational numbers between 1 and 2
Solution:
Given that to find out 5 rational numbers between 1 and 2
Rational number lying between 1 and 2
$=\frac{1+2}{2}$
$=\frac{3}{2}$
$=1<\frac{3}{2}<2$
Rational number lying between 1 and $\frac{3}{2}$
$=\frac{1+\frac{3}{2}}{2}$
$=\frac{5}{4}$
$=1<\frac{5}{4}<\frac{3}{2}$
Rational number lying between 1 and $\frac{5}{4}$
$=\frac{1+\frac{5}{4}}{2}$ Rational number lying between $\frac{3}{2}$ and 2
$=\frac{9}{8}$
$=1<\frac{9}{8}<\frac{5}{4}$
Rational number lying between $\frac{3}{2}$ and 2
$=\frac{\frac{3}{2}+2}{2}$
$=\frac{7}{4}$
$=\frac{3}{2}<\frac{7}{4}<2$
Rational number lying between $\frac{7}{4}$ and 2
$=\frac{\frac{7}{4}+2}{2}$
$=\frac{15}{8}$
$=\frac{7}{4}<\frac{15}{8}<2$
Therefore, $1<\frac{9}{8}<\frac{5}{4}<\frac{3}{2}<\frac{7}{4}<\frac{15}{8}<2$

Q3. Find out 6 rational numbers between 3 and 4
Solution:
Given that to find out 6 rational numbers between 3 and 4
We have,
$3 \times \frac{7}{7}=\frac{21}{7}$ and
$4 \times \frac{6}{6}=\frac{28}{7}$
We know $21<22<23<24<25<26<27<28$
$\frac{21}{7}<\frac{22}{7}<\frac{23}{7}<\frac{24}{7}<\frac{25}{7}<\frac{26}{7}<\frac{27}{7}<\frac{28}{7}$
$3<\frac{22}{7}<\frac{23}{7}<\frac{24}{7}<\frac{25}{7}<\frac{26}{7}<\frac{27}{7}<4$
Therefore, 6 rational numbers between 3 and 4 are
$\frac{22}{7}, \frac{23}{7}, \frac{24}{7}, \frac{25}{7}, \frac{26}{7}, \frac{27}{7}$
Similarly to find 5 rational numbers between 3 and 4, multiply 3 and 4 respectively with $\frac{6}{6}$ and in order to find 8 rational numbers between 3 and 4 multiply 3 and 4 respectively with $\frac{8}{8}$ and so on.

Q4. Find 5 rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$
Solution :
Given to find out the 5 rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$
To find 5 rational numbers between $\frac{3}{5}$ and $\frac{4}{5}, \frac{3}{5}$ and $\frac{4}{5}$ with $\frac{6}{6}$
We have,
$\frac{3}{5} \times \frac{6}{6}=\frac{18}{30}$
$\frac{4}{5} \times \frac{6}{6}=\frac{24}{30}$
We know $18<19<20<21<22<23<24$
$\frac{18}{30}<\frac{19}{30}<\frac{20}{30}<\frac{21}{30}<\frac{22}{30}<\frac{23}{30}<\frac{24}{30}$
$\frac{3}{5}<\frac{19}{30}<\frac{20}{30}<\frac{21}{30}<\frac{22}{30}<\frac{23}{30}<\frac{4}{5}$
Therefore, 5 rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ are $\frac{19}{30}, \frac{20}{30}, \frac{21}{30}, \frac{22}{30}, \frac{23}{30}$

Q5. Answer whether the following statements are true or false? Give reasons in support of your answer.
(i) Every whole number is a rational 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
Solution:
(i) True. As whole numbers include and they can be represented
For example $-\frac{0}{10}, \frac{1}{1}, \frac{2}{1}, \frac{3}{1} \ldots .$ And so on.
(ii) True. As we know $1,2,3,4$ and so on, are integers and they can be represented in the form of $\frac{1}{1}, \frac{2}{1}, \frac{3}{1} \frac{4}{1}$.
(iii) False. Numbers such as $\frac{3}{2}, \frac{1}{2}, \frac{3}{5}, \frac{4}{5}$ are rational numbers but they are not integers.
(iv) True. Whole numbers include all of the natural numbers.
(v) False. As we know whole numbers are a part of integers.
(vi) False. Integers include $-1,-2,-3$ and so on…… which is not whole number

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