RS Aggarwal Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1C

R S Aggarwal Solutions for Class 10 Maths Chapter 1 Real Numbers, contains solutions for all Exercise 1C questions. Class 10 real numbers Exercise 1C based on the concept of rational numbers and their properties. All these questions are solved by subject experts using step by step problem-solving approach. R S Aggarwal Solutions of Class 10 and start practising.

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Rs Aggarwal Solution Class 10 Maths Chapter 1 Ex 1C
Rs Aggarwal Solution Class 10 Maths Chapter 1 Ex 1C
Rs Aggarwal Solution Class 10 Maths Chapter 1 Ex 1C
Rs Aggarwal Solution Class 10 Maths Chapter 1 Ex 1C
Rs Aggarwal Solution Class 10 Maths Chapter 1 Ex 1C
Rs Aggarwal Solution Class 10 Maths Chapter 1 Ex 1C

 

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Exercise 1C Page No: 24

Question 1: Without actual division, show that each of the following rational number is a terminating decimal. Express each in decimal form.

(i)

rs aggarwal class 10 maths chapter 1 ex c img 1

(ii) 24/125

(iii) 171/800

(iv) 15/1600

(v) 17/320

(vi) 19/3125

Solution:

rs aggarwal class 10 maths chapter 1 ex c img 1

Clearly either 2 or 5 is not a factor of 23, So given fraction is in its simplest form.

Given fraction already in the form of (2m × 5n).

Hence, the given rational is terminating.

We can written it as:

= 0.115

(ii) 24/125

Denominator = 125 = 53

5 is not a factor of 24, so fraction is in its simplest form.

Also written in the form:

24/125 = 24/(20 x 53 ), which is similar to the form of (2m × 5n).

So, fraction is in the form of (2m × 5n).

Hence, the given rational is terminating.

24/125 = 0.192

(iii) 171/800

Denominator = 180 = 25 x 52

Either 2 or 5 is not a factor of 171, so fraction in its simplest form.

Also written in the form:

24/125 = 171/(25 x 52), which is similar to the form of (2m × 5n).

So, fraction is in the form of (2m × 5n).

Hence, the given rational is terminating.

171/800 = 0.21375

(iv) 15/1600

Denominator = 1600 = 26 x 52

Either 2 or 5 is not a factor of 15.

So the fraction in its simplest form.

Also written in the form:

15/1600 = 15/(26 x 52), which is similar to the form of (2m × 5n).

So, fraction is in the form of (2m × 5n).

Hence, the given rational is terminating.

15/1600 = 0.009375

(v) 17/320

Denominator = 320 = 26 x 5

Either 2 or 5 is not a factor of 17.

So the fraction in its simplest form.

Also written in the form:

17/320= 17/(26 x 5), which is similar to the form of (2m × 5n).

So, fraction is in the form of (2m × 5n).

Hence, the given rational is terminating.

17/320 = 0.053125

(vi) 19/3125

Denominator = 3125 = 55

Either 2 or 5 is not a factor of 19.

So the fraction in its simplest form.

Also written in the form:

19/3125 = 19/(20 x 55), which is similar to the form of (2m × 5n).

So, fraction is in the form of (2m × 5n).

Hence, the given rational is terminating.

19/3125 = 0.00608

Question 2: Without actual division, show that each of the following rational numbers is a non-terminating repeating decimal:

(i)

rs aggarwal class 10 maths chapter 1 ex c img 2

(ii)

rs aggarwal class 10 maths chapter 1 ex c img 3

(iii)

rs aggarwal class 10 maths chapter 1 ex c img 4

(v)77/210
(vi) 32/147
(vii) 29/343
(viii) 64/455

Solution:

(i)

rs aggarwal class 10 maths chapter 1 ex c img 2

2 or 3 is not a factor of 11, so fraction is in its simplest form.

And, (23 x 3) ≠ (2m x 5n)

Hence, the given fraction is non-terminating repeating decimal.

(ii)

rs aggarwal class 10 maths chapter 1 ex c img 3

2, 3 or 5 is not a factor of 73, so fraction is in its simplest form.

And, (22 × 33 × 5) ≠ (2m x 5n)

Hence, the given rational is non-terminating repeating decimal.

(iii)

rs aggarwal class 10 maths chapter 1 ex c img 4

2, 5 or 7 is not a factor of 129, so fraction is in its simplest form.

And, (22 × 57 × 75) ≠ (2m x 5n)

Hence, given fraction is non-terminating repeating decimal.


(iv)9/35

5 or 7 is not a factor of 9, so fraction is in its simplest form.

And, (5 × 7) ≠ (2m x 5n)

 Hence, the given fraction is non-terminating repeating decimal.

(v)77/210

2, 3 or 5 is not a factor of 11, so given fraction is in its simplest form.

And, (2 × 3 × 5) ≠ (2m x 5n)

Hence, the given fraction is non-terminating repeating decimal.

(vi) 32/147

3 or 7 is not a factor of 32, so fraction is in its simplest form.

And, (3 × 72) ≠ (2m x 5n)

Hence, the given fraction is non-terminating repeating decimal.


(vii) 29/343

7 is not a factor of 29, so fraction is in its simplest form. And,  73 ≠ (2m x 5n)

Hence, the given fraction is non-terminating repeating decimal.

(viii) 64/455

5, 7 or 13 is not a factor of 64, so it is in its simplest form. And, (5 × 7 × 13) ≠ (2m x 5n)

 Hence, the given fraction is non-terminating repeating decimal.

Question 3: Express each of the following as a fraction in simplest form:

rs aggarwal class 10 maths chapter 1 ex c img 5

Solution:

(i)

rs aggarwal class 10 maths chapter 1 ex c img 6

(ii)

rs aggarwal class 10 maths chapter 1 ex c img 7

(iii)

rs aggarwal class 10 maths chapter 1 ex c img 8

(iv)

rs aggarwal class 10 maths chapter 1 ex c img 9

(v)

rs aggarwal class 10 maths chapter 1 ex c img 10

(vi)

rs aggarwal class 10 maths chapter 1 ex c img 11

 
Exercise 1A Solutions : 10 Questions (Short Answers)

Exercise 1B Solutions : 27 Questions (Short Answers)

Exercise 1D Solutions : 11 Questions (Short Answers)

Exercise 1E Solutions : 23 Questions (Short Answers)

RS Aggarwal Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1C

Class 10 Maths Chapter 1 Real Numbers Exercise 1C, based on the following topics and subtopics:

  • Rational Numbers
  • Some Important results on rational numbers