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.

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

RBSE Solutions For Class 10 Maths Chapter 2 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

RBSE Solutions For Class 10 Maths Question 2.
Write down the decimal expansion of the following (RBSESolutions.com) rational numbers and show whether these are terminating.
(i) \(\frac { 13 }{ 125 }\)
(ii) \(\frac { 14588 }{ 625 }\)
(iii) \(\frac { 59 }{ 500 }\)
Solution

RBSE Solutions For Class 10 Maths Chapter 2 Miscellaneous 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) \(27.\bar { 142857 }\)
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 \(\frac { p }{ q }\)
So, this number is not rational number
(ii) 43.123456789 = \(\frac { 43123456789 }{ 1000000000 }\)
This number is of the form \(\frac { p }{ q }\)
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) \(27.\bar { 142857 }\)
= 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 \(\frac { p }{ q }\)
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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