Here we are giving you the solution of NCERT Solutions for Class 10 Mathematics Chapter 1 Real Numbers Ex 1.4 . You can also download Free NCERT Solutions for Class 10 Maths Chapter 1 PDF on our website . NCERT Maths class 10 chapter 1 exercise 1.4 solutions This post has been prepared by the experienced teachers of Educationforindia.com . Detailed answers of all the questions in Class 10th Maths Chapter 1

## Class 10 Maths Chapter 1 Real Numbers Ex 1.4

**Exercise 1.4 class 10th Question 1**

**1. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:**

**(i) \frac{\mathbf{13}}{\mathbf{3125}} (ii) \frac{\mathbf{17}}{\mathbf{8}} (iii) \frac{\mathbf{64}}{\mathbf{455}} (iv) \frac{\mathbf{15}}{\mathbf{1600}} (v) \frac{\mathbf{29}}{\mathbf{343}} **

**(iv) 23/2 ^{3 }5^{2 }(vii) 129/2^{2 }5^{7} 7^{5 } (viii) \frac{\mathbf{6}}{\mathbf{15}} (ix) \frac{\mathbf{35}}{\mathbf{50}} (x) \frac{\mathbf{77}}{\mathbf{210}}**

__Solution:__

According to the theory we will take x = \frac{p}{q} as a rational number, and the prime factorization will be in the form 2^{n }5^{m}. Note that here, n and m are non- negative integers. Then x will have a decimal expression which terminates.**(i)** **\frac{\mathbf{13}}{\mathbf{3125}} **

By factorizing the denominator we will get,

3125 = 5x5x5x5x5 = 5^{5}

Here, the denominator is in the form of 5^{m }so, \frac{\mathbf{13}}{\mathbf{3125}} is terminating.**(ii)** ** \frac{\mathbf{17}}{\mathbf{8}}**

By factorizing the denominator we will get,

8 = 2x2x2= 2

^{3}

Here, the denominator is in the form of 2

^{n }so, \frac{\mathbf{17}}{\mathbf{8}} is terminating

**(iii)**

**\frac{\mathbf{64}}{\mathbf{455}}**

By factorizing the denominator we will get,

455 = 5x7x13

Here, the denominator is in the form of 2

^{n }5

^{m }so, \frac{\mathbf{64}}{\mathbf{455}} is not terminating

**(iv)**

**\frac{\mathbf{15}}{\mathbf{1600}}**

By factorizing the denominator we will get,

1600 = 2x2x2x2x2x2x5x5 = 2

^{6 }5

^{2}

Here, the denominator is in the form of 2

^{n }5

^{m }so, \frac{\mathbf{15}}{\mathbf{1600}} is terminating

**(v)**

**\frac{\mathbf{29}}{\mathbf{343}}**

By factorizing the denominator we will get,

343 = 7x7x7 = 7

^{3}

Here, the denominator is in the form of 2

^{n }5

^{m }so, \frac{\mathbf{29}}{\mathbf{343}} is terminating

**(iv) 23/2**

^{3 }5^{2}Here, the denominator is in the form of 2

^{n }5

^{m }so,

**23/2**is terminating

^{3 }5^{2 }23/2^{3 }5^{2 }**(vii) 129/2**

^{2 }5^{7}7^{5 }Here, the denominator is in the form of 2

^{n }5

^{m }so,

**129/2**is not terminating

^{2 }5^{7}7^{5 }**(viii)**

**\frac{\mathbf{6}}{\mathbf{15}}**

Let’s divide both the numerator and denominator by 3 and we will get \frac{\mathbf{3}}{\mathbf{15}}

that is why the denominator is in the form of 5

^{m}so, \frac{\mathbf{6}}{\mathbf{15}} is terminating.

**(ix)**

**\frac{\mathbf{35}}{\mathbf{50}}**

Let’s divide both the numerator and denominator by 5 and we will get \frac{\mathbf{7}}{\mathbf{10}}

now factorize the denominator and we will get

10 = 2×5

Here, the denominator is in the form of 2

^{n }5

^{m }so, \frac{\mathbf{35}}{\mathbf{50}} is terminating

**(x)**

**\frac{\mathbf{77}}{\mathbf{210}}**

Let’s divide both the numerator and denominator by 7 and we will get \frac{\mathbf{11}}{\mathbf{30}}

now factorize the denominator and we will get

30 = 2x3x5

Here, the denominator is not in the form of 2

^{n }5

^{m }so, \frac{\mathbf{77}}{\mathbf{210}} is non-terminating repeating

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