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CLASS 9TH MATHS- Q2- EX-1.6- CH-1 - NUMBER SYSTEM | MATHS CBSE CLASS 9TH NCERT QUESTIONS SOLUTIONS Apni ClassRoom By Er. Deepak Garg

class 9th exercise 1.6 question number 2,
class 9 maths chapter 1 number system exercise 1.6 question 2,



1
7
= 0142857 . . Can you predict what the decimal expansions of
2
7
,
3
7
,
4
7
,
5
7
,
6
7
are, without actually doing the long division? If so, how?
[Hint : Study the remainders while finding the value of
1
7
carefully.]
3. Express the following in the form p
q
, where p and q are integers and q ≠ 0.
(i) 0 6. (ii) 0 47 . (iii) 0 001 .
4. Express 0.99999 .... in the form p
q
. Are you surprised by your answer? With your
teacher and classmates discuss why the answer makes sense.
5. What can the maximum number of digits be in the repeating block of digits in the
decimal expansion of
1
17 ? Perform the division to check your answer.
6. Look at several examples of rational numbers in the form p
q
(q ≠ 0), where p and q are
integers with no common factors other than 1 and having terminating decimal
representations (expansions). Can you guess what property q must satisfy?
7. Write three numbers whose decimal expansions are non-terminating non-recurring.
8. Find three different irrational numbers between the rational numbers
5
7
and
9
11
.
9. Classify the following numbers as rational or irrational :
(i) 23 (ii) 225 (iii) 0.3796
(iv) 7.478478... (v) 1.101001000100001...

EXERCISE 1.4
1. Visualise 3.765 on the number line, using successive magnification.
2. Visualise 4 26 . on the number line, up to 4 decimal places.



EXERCISE 1.5
1. Classify the following numbers as rational or irrational:
(i) 2 5 − (ii) (3 23 23 + −) (iii)
2 7
7 7
(iv)
1
2
(v) 2π
2. Simplify each of the following expressions:
(i) (3 3 2 2 + + ) ( ) (ii) (3 3 3 3 + − ) ( )
(iii) ( )
2
5 2 + (iv) ( 5 2 5 2 − + ) ( )
3. Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter
(say d). That is, π =
c
d
⋅ This seems to contradict the fact that π is irrational. How will
you resolve this contradiction?
4. Represent 9 3. on the number line.
5. Rationalise the denominators of the following:
(i)
1
7
(ii)
1
7 6 −
(iii)
1
5 2 +
(iv)
1
7 2
EXERCISE 1.6
1. Find : (i)
1
2 64 (ii)
1
5 32 (iii)
1
3 125
2. Find : (i)
3
2 9 (ii)
2
5 32 (iii)
3
4 16 (iv)
1
3 125
−
3. Simplify : (i)
2 1
3 5 2 2⋅ (ii)
7
3
1
3
      (iii)
1
2
1
4
11
11
(iv)
1 1
2 2 7 8
Hello students, in this chapter you are going to learn Number System.

We will go topic wise

NUMBER SYSTEMS
1 ) Irrational Numbers
2 ) Real Numbers and their Decimal Expansions
3) Representing Real Numbers on the Number Line
4) Operations on Real Numbers
5) Laws of Exponents for Real Numbers


The collection of numbers is called the Number system. These numbers are of different types such as natural numbers, whole numbers, integers, rational numbers and irrational numbers. Let us see the table below to understand with the examples.

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