RBSE Solutions for Class 10 Maths Chapter 2 Real Numbers Ex 2.4

RBSE Solutions for Class 10 Maths Chapter 2 Real Numbers Ex 2.4 is part of RBSE Solutions for Class 10 Maths. Here we have given Rajasthan Board RBSE Class 10 Maths Chapter 2 Real Numbers Exercise 2.4.

Board	RBSE
Te×tbook	SIERT, Rajasthan
Class	Class 10
Subject	Maths
Chapter	Chapter 2
Chapter Name	Real Numbers
E×ercise	Exercise 2.4
Number of Questions Solved	3
Category	RBSE Solutions

Rajasthan Board RBSE Class 10 Maths Chapter 2 Real Numbers Ex 2.4

Question 1.
Without actually performing the long (RBSESolutions.com) division method, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Solution

Question 2.
Write down the decimal expansion of the following (RBSESolutions.com) rational numbers and show whether these are terminating.
(i) [latex]\frac { 13 }{ 125 }[/latex]
(ii) [latex]\frac { 14588 }{ 625 }[/latex]
(iii) [latex]\frac { 59 }{ 500 }[/latex]
Solution

Question 3.
For the following decimal expansions, decide whether (RBSESolutions.com) these are rational or not. If these are rational, then write the note on prime factors of its denominator.
(i) 0.120120012000120000…
(ii) 43.123456789
(iii) [latex]27.\bar { 142857 }[/latex]
Solution
(i) 0.120120012000120000…
The decimal expansion of this number is non-terminating and non-repeating So it cannot be written in the form of [latex]\frac { p }{ q }[/latex]
So, this number is not rational number
(ii) 43.123456789 = [latex]\frac { 43123456789 }{ 1000000000 }[/latex]
This number is of the form [latex]\frac { p }{ q }[/latex]
This is a rational number
q = 1000000000 = (10)⁹ = (2 x 5)⁹ = 2⁹ x 5⁹
So, prime factor of q is 2 and 5.
(iii) [latex]27.\bar { 142857 }[/latex]
= 27.142857 142857 142857…
The decimal expansion of this number is (RBSESolutions.com) non-terminating and recurring.
So, it can be written in the form [latex]\frac { p }{ q }[/latex]
This is a rational number.
So, besides 2 and 5, one other prime factor of q other prime positive integers is possible.

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