**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

Thus, the decimal expansion of 1/11 is non-terminating repeating decimal.

**(iii)** We have, 4^{1}/_{8} = 33/8

Dividing 33 by 8, we get

^{1}/

_{8}= 4.125. Thus, the decimal expansion of 4

^{1}/

_{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

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} × 5^{n}, 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 = 15

^{2}

∴ 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.

**Related Links:**

**NCERT Solutions for Maths Class 10**