Exercise 1.4 Class 10 Maths Real Numbers Complete Solutions estudynow

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Exercise 1.4 class 10 maths

Exercise 1.4 Class 10 Maths

exercise 1.4 class 10 maths ncert solutions

Class 10 Maths Exercise 1.4 solution : We are providing Class 10 Maths solutions  for 1st chapter ex 1.4 class 10 maths “Real Numbers” textbook provided by NCERT for SEBA, CBSE etc complete exercise solutions with Additional Most Important Questions in our website – online, absolutely for FREE for everyone. No need to do any sign in process, just browse and enjoy all of the Class 10 Maths Chapter 1 exercise 1.4 solutions from us. From the First exercise “Real Numbers”, there are total 4 exercise given in bellow table. Click on the exercise number to browse the complete solutions from ex 1.4 class 10 ..

Go to Real Numbers Exercise 1.1

Go to Real Numbers Exercise 1.2

Go to Real Numbers Exercise 1.3

You are at Real Numbers Exercise 1.4

Sub-Contents of “Chapter 1 Real Numbers” : There are  total 6 sub contents exists in Class 10 maths chapter 1 Real Numbers. We need to study all of the sub-contents first. The Sub Contents are-

  1. Introduction
  2. Euclid’s Division algorithm
  3. The Fundamental Theorem of Arithmetic
  4. Revisiting Irrational Numbers
  5. Revisiting Rational Numbers & Their Decimal Expansion
  6. Summary
FROM LATEST UPDATED NCERT SYLLABUS

 

Exercise 1.4 Class 10 Maths

Real Numbers

Class 10 Maths Exercise 1.4 Question 1

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

(i) \cfrac {13} {3125}     (ii) \cfrac {17} {8}    (iii) \cfrac {64} {455}    (iv) \cfrac {15} {1600}

(v) \cfrac {29} {343}    (vi) \cfrac {23} {2³×5²}  

 (vii) \cfrac {129} {2²× 5^7 ×7^5}

(viii) \cfrac {6} {15}   (ix) \cfrac {35} {50}   (x) \cfrac {77} {210}

Solutions: (i) \cfrac {13} {3125}  

Here, Denominator = 3125 = 5 × 5 × 5 × 5 × 5

So, The denominator consists prime factor = 5 , which is in the form 2^n × 5^m , where n = 0 , m = 5

So, \cfrac {13} {3125} has terminating decimal expansion.

(ii) \cfrac {17} {8}  

Here, Denominator = 8 = 2 × 2  × 2

Which is in the form 2^n × 5^m , where n = 3 , m = 0

So, \cfrac {17} {8}   has a terminating decimal expansion.

(iii) \cfrac {64} {455}

Here, Denominator = 455 = 5 × 7 × 13

Means, In addition to 5, 7 & 13 are also two factor of the denominator of the given fraction. So, The given fraction will have a non-terminating decimal fraction.

(iv) \cfrac {15} {1600}

Here Denominator = 1600 = 2 × 2 × 2  × 2 × 2 × 2 × 5 × 5

So, The denominator consists prime factor = 5 & 2 only , which is in the form 2^n × 5^m , where n = 6 , m = 2 . Decimal expansion is ternimating.

(v) \cfrac {29} {343}

Denominator = 343 = 7 × 7 × 7

So, The denominator consists prime factor = 7 only , which is’t in the form 2^n × 5^m . The decimal expansion of the given fraction will be non terminating.

SEE ALL THE HINTS IN BELLOW PORTION

(vi) \cfrac {23} {2³×5²}

Here clearly, The denominator consists prime factor = 5 & 2 only , which is in the form 2^n × 5^m , where n = 3 , m = 2 . Decimal expansion is ternimating.

(vii) \cfrac {129} {2²× 5^7 ×7^5}

Here clearly, The denominator consists prime factor = 2, 5 and also 7 , which is’t in the form 2^n × 5^m only. So, The decimal expansion of the given fraction will be non terminating.

(viii) \cfrac {6} {15} = \frac 25

So, The denominator consists prime factor = 5 , which is in the form 2^n × 5^m , where n = 0 , m = 1 . So, the given fraction has a terminating decimal expansion.

(ix) \cfrac {35} {50}

Denominator = 50 = 2 × 5 × 5 

So, The denominator consists prime factor = 2 & 5 , which is in the form 2^n × 5^m , where n = 1 , m = 2 . So, the given fraction has a terminating decimal expansion.

(x) \cfrac {77} {210} = \cfrac {11} {30}

Denominator = 30 = 2 × 3 × 5

So, The denominator consists prime factor = 2, 5 but 3 also , which is’t in the form 2^n × 5^m . The decimal expansion of the given fraction will be non terminating.


Class 10 Maths Exercise 1.4 Question 3

The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If, they are rational, and of the form \frac p q , what can you say about the prime factors of q?

(i) 43.123456789

(ii) 0.1201120012000120000…

(iii) 43.\overline{123456789}

Solutions: (i) For this number, we can count the total number of digits after the decimal which is = 9 . That means, this number can be expressed in the form \frac p q easily, where q ≠ 0 . So, Clearly, this decimal number is a rational number.

(ii) For this number–

  1. we can’t count the total number of digits after the decimal.
  2. digits after the decimal are not repeating uniformly.

That means, this number can’t be expressed in the form \frac p q easily, where q ≠ 0 . So, Clearly, this decimal number is a irrational number.

(iii) For this number–

  1. we can’t count the total number of digits after the decimal.
  2. But, digits after the decimal are repeating uniformly ( uperline means repeating).

That means, this number can be expressed in the form \frac p q easily, where q ≠ 0 . So, Clearly, this decimal number is a rational number.

 

Additional Questions From Ex 1.4 Class 10:

We have listed some additional questions from this ex 1.4 class 10 maths Real Numbers bello. Practice these questions yourself. Please commment down bellow if you can’t solved them. Also, These questions are some of most important questions with very high probability in final exams. solve now-

1.In Which of the following rational number can be expressed as a terminating decimal?

(A) \cfrac {13} {25}    (B)  \cfrac {2} {15}    (C) \cfrac {17} {18}    (D) \cfrac {77} {210}

2. In the following real numbers which one is non terminating decimal expansion?

(A) √3    (B) π    (C)  \cfrac {1} {17}     (D) \cfrac {13} {125}

3. Choose the rational number from the followiong.

(A) \cfrac {1} {√2}     (B) 3√4    (C) 7√5    (D)  3 + √2

4. The number of decimal places after which the decimal expansion of the rational number \cfrac {33} {2 × 5²} will terminate is —

(A) 2       (B) 1      (C)  3         (D) 4

5. If n is any natural number, then which of the following expression ends with 0?

(A) (3 × 2)^n                (B) (4 × 3)^n 

(C) (2 × 5)^n                (D)  (5 × 3)^n 

Steps To Recognise Terminating or Non-Terminating:

Bellow is the complete rules with short tricks how you can say that a fraction will be a terminating decimal expression or non-terminating:

  • Just Check out the denominator of the Fraction.
  • Factorise the denominator
  • See what you found –
  • If you found the primes factors as only 2 or only 5 or 2 and 5 only, and no any other prime number, then obviousely, the denominator can be expressed as 2^n × 5^m otherwise NOT

If you can expressed the denominator as 2^n × 5^m , then the decimal expansion of the fraction will be terminating.  On the other hand, if you found any numbers other than 2 and 5, which cannot be cancelled with the numerator, then the decimal expansion of the fraction will be Non – terminating. That’s it. Hope you enjoyed all the ex 1.4 class 10 ncert solutions from estudynow.com.

NCERT SOLUTIONS FOR CLASS 10 MATHS :

We are providing complete Class 10 Maths Solution . You can get complete and updated solution from our website. Please click on your prefered chapter bellow from NCERT CLASS 10 MATHS and see the solutions. You can get complete ncert solutions for class 10 maths from here. 

1 Chapter 1  Real Numbers
2 Chapter 2  Polynomials
3 Chapter 3  Pair of Linear Equations in Two Variables
4 Chapter 4  Quadratic Equations
5 Chapter 5  Arithmetic Progressions
6 Chapter 6  Triangles
7 Chapter 7  Co-ordinate Geometry
8 Chapter 8  Introduction to trigonometry
9 Chapter 9  Application of Trigonometry
10 Chapter 10  Circle
11 Chapter 11  Constructions
12 Chapter 12  Area Related to Circles
13 Chapter 13  Surface area and volumes
14 Chapter 14 Statistics
15 Chapter 15 Probability

 

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