NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3 are the part of NCERT Solutions for Class 9 Maths. Here you can find the NCERT Solutions for Class 9 Maths Chapter 1 Number System 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

∴ 4¹/₈ = 4.125. Thus, the decimal expansion of 4¹/₈ is a terminating decimal.

(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

∴ 2/11 = 0.1818…
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 2^m × 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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NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3

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