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Classify the following numbers as rational or irrational : (i)  (ii)  (iii) 0.3796 (iv) 7.478478... (v) 1.101001000100001...

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(i) As the decimal expansion of this number is non-terminating non-recurring, therefore, it is an irrational number. (ii) It is a rational number as it can be represented in form. (iii) 0.3796 As the decimal expansion of this number is terminating, therefore, it is a rational number. (iv) 7.478478...
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(i) 

As the decimal expansion of this number is non-terminating non-recurring, therefore, it is an irrational number.

(ii) 

It is a rational number as it can be represented in  form.

(iii) 0.3796

As the decimal expansion of this number is terminating, therefore, it is a rational number.

(iv) 7.478478 … 

As the decimal expansion of this number is non-terminating recurring, therefore, it is a rational number.

(v) 1.10100100010000 …

As the decimal expansion of this number is non-terminating non-repeating, therefore, it is an irrational number.

 
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