Q. 94.0( 48 Votes )

Without actually

Answer :

(i). We have


Therefore, it clearly is non-terminating decimal. (since, it is recurring or repeating).


Justification:


First, converting it in the form p/q, where p and q are integers and q ≠ 0.


So, let .


That is, x = 0.55555… …(i)


Multiply 10 by equation (i),


10 × x = 10 × 0.55555…


10x = 5.55555… …(ii)


Subtracting equations (i) from (ii), we get


10x – x = 5.5555… - 0.5555…


9x = 5


x = 5/9


Now, by factorizing the denominator, we get


9 = 3 × 3 = 32


Denominator is not in the form of 2n × 5n.


is non-terminating.


(ii). We have 11/18.


Now, without actual division, we got to factorize the denominator of the rational number.


By factorizing the denominator, we get


18 = 2 × 3 × 3


18 = 2 × 32


Denominator is not in the form of 2n × 5n.


11/18 is non-terminating.


(iii). We have 13/20.


Now, without actual division, we got to factorize the denominator of the rational number.


By factorizing the denominator, we get


20 = 2 × 2 × 5


20 = 22 × 51


Denominator is in the form of 2n × 5n (i.e., 22 × 51)


13/20 is terminating decimal.


(iv). We have 41/42.


Now, without actual division, we got to factorize the denominator of the rational number.


By factorizing the denominator, we get


42 = 2 × 3 × 7


Denominator is not in the form of 2n × 5n.


41/42 is non-terminating.


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