Here we are trying to give the number system class 9 important extra questions along with answer. It tests the basic concepts and at the same makes the student comfortable with the questions

Question 1
Represent each number on number line 8/3 , 1.3 , -24 , 23/6

Question 2
Find a rational number lying between (i) 0.75 and 1.2 (ii) -3/4 and-2/5 Answer

Rational number between two number can be find using mean method
(i) Mean of 0.75 and 1.2 = $\frac {.75 + 1.2}{2}= .975$
So .975 is the rational lying between 0.75 and 1.2
(ii) Mean of -3/4 and -2/5 = $\frac {(-3/4) + (-2/5)}{2}= \frac {-23}{40}$
So $\frac {-23}{40}$ is the rational number

Question 3
Insert six rational numbers. between 3 and 4 Answer

3.1,3.2,.3.3,3.4,3.5,3.6

Question 4
Insert 16 rational numbers. between 2.1 and 2.2 Answer

Question 6
Locate the number √5 , √10 , √17 on Number line

Question 7
Find which of the variables x, y, z and u represent rational numbers and which irrational numbers:
(i)x^{2} =11
(ii)y^{2} =36
(iii)z^{2} = .04
(iv) u^{2} = 19/9 Answer

(i) x=√ 11, So it is irrational Number
(ii) y=6, So it is rational number
(iii) z==.2, So it is rational number
(iv) u = √19/3, So it is rational number

Question 8
Find an irrational number between 1/7 and 2/7 Answer

$\frac {1}{7}=.142857142857.....= 0.\overline{142857}$
$\frac {2}{7}=.285714285714.....= 0.\overline{285714}$
Now we know that a irrational number is a non-terminating and non repeating number, So irrational number between these can be
.162857147647222977....
or
.17285716786222977....

Question 9
Which is of these is the rational number between √2 and √3
(i) (√2 + √3)/2
(ii) 1.5
(iii) 1.8
(iv) (√2 . √3)/2 Answer

Answer is (i)

Question 10
Express $0.\overline{36}$ and $0.5\overline{6}$ in the simplest form of rational no Answer

(i)$0.\overline{36}=0.363636..$
Let $x = 0.363636.$
$100x = 36.363636.$
$100x = 36 + x$
$99x = 36$
$x = \frac {36}{99}$
(ii)$0.5\overline{6}=0.56666..$
Let $x = 0.56666..$
$10x = 5.666666....= 5 + 0.\overline{6}$
Now let $y=0.\overline{6}$
$10y=6.6666..=6+y$
or $y=\frac {6}{9}$
So $10x = 5 + \frac {6}{9}$
$x=\frac {51}{90}= \frac {17}{30}$

Question 11 Cross-word Puzzle

Across
3. rational numbers have only two choices- either they are terminating or non-terminating ________
6. The First person to discover the numbers which were not rational
7. The number (√3 -1)(√3 +1) is
8. Counting Number are called Down
1. Non-terminating non recurring decimal expression
2. The set of positive and negative number is
4. Number of the form p/q
5. Who was the first to compute digits in the decimal expansion of π(Greek genius ) Answers

This Number System Class 9 Important questions with answers is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.

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