- NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1
- NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2
- NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3
- NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.4
- NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.5
NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3
Ex 1.3 Class 9 Maths Question 1.
Write the following in decimal form and say what kind of decimal expansion each
has
Solution:
(i) We have, 36/100 = 0.36
Thus, the decimal expansion of 36/100 is a
terminating decimal.
(ii) 1/11
Dividing 1 by 11, we get
Thus, the decimal expansion of 1/11 is non-terminating repeating decimal.
(iii) We have, 41/8 = 33/8
Dividing 33 by 8, we get
(iv) 3/13
Dividing 3 by 13, we get
∴ 3/13 =
0.230769230769…
Here, the repeating block of digits is 230769.
Thus, the decimal expansion of 3/13 is non-terminating repeating decimal.
(v) 2/11
Dividing 2 by 11, we get
Here, the repeating block of digits is 18.
Thus, the decimal expansion of 2/11 is non-terminating repeating decimal.
(vi) 329/400
Dividing 329 by 400, we get
∴ 329/400 =
0.8225.
Thus, the decimal expansion of 329/400 is terminating decimal.
Ex 1.3 Class 9 Maths Question 2.
Solution:
Ex 1.3 Class 9 Maths Question 3.
Solution:
Ex 1.3 Class 9 Maths Question
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.
Solution:
Let x =
0.99999….. …. (i)
As there is
only one repeating digit, multiplying (i) by 10 on both sides, we get
10x =
9.9999….. .… (ii)
Subtracting
equation (i) from (ii), we get
10x – x =
(9.9999…..) — (0.9999…..)
⇒ 9x = 9
⇒ x = 9/9 = 1
⇒ x = 1
Thus,
0.9999….. = 1
As 0.9999…..
goes on forever, there is no such a big difference between 1 and 0.9999…..
Hence, both
are equal.
Ex 1.3 Class 9 Maths Question
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.
Solution:
In 1/17, the divisor is 17.
Since, the
number of entries in the repeating block of digits is 1 less than the divisor,
then the maximum number of digits in the repeating block is 16.
Dividing 1
by 17, we have
The remainder 1 is the same digit from which we
started the division.
∴ 1/17 = 0.058823529411764705882……
Thus, there are 16 digits in the repeating block in the decimal expansion
of 1/17.
Hence, our answer is verified.
Ex 1.3 Class 9 Maths Question 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?
Solution:
Let us find the decimal
expansion of the following terminating rational numbers:
We observe
from the above decimal expansions that the prime factorisation of q (i.e.,
denominator) has only powers of 2 or powers of 5 or powers of both.
We can say that the prime factorisation of q must be in the
form 2m × 5n, where m and m are whole numbers.
Ex 1.3 Class 9
Maths Question 7.
Write three numbers whose
decimal expansions are non-terminating non-recurring.
Solution:
√2 = 1.414213562 ……
√3 = 1.732050808 ……
√5 = 2.23606797 ……
Ex 1.3 Class 9 Maths Question 8.
Find three different
irrational numbers between the rational numbers 5/7 and 9/11 .
Solution:
We have,
Three irrational numbers between 5/7 and 9/11 are
(i) 0.750750075000 …..
(ii) 0.767076700767000 ……
(iii) 0.78080078008000 ……
Ex 1.3 Class 9 Maths Question 9.
Classify the following
numbers as rational or irrational
(i) √23
(ii) √225
(iii) 0.3796
(iv) 7.478478…..
(v) 1.101001000100001………
Solution:
(i) ∵ 23 is not a perfect square.
∴ √23 is an
irrational number.
(ii) ∵ 225 = 15 x 15 = 152
∴ 225 is a perfect square.
Thus, √225 is a rational number.
(iii) ∵ 0.3796 is a terminating decimal.
∴ It is a rational number.
(iv) 7.478478…
Since, 7.478478… is a non-terminating recurring
(repeating) decimal.
∴ It is a rational number.
(v) Since,
1.101001000100001… is a non-terminating, non-repeating decimal number.
∴ It is an irrational number.
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