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Q.

Which numbers have their decimal expansions non-terminating and  non-repeating?


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a

Rational numbers

b

Natural numbers

c

Irrational numbers

d

Whole numbers 

answer is C.

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Detailed Solution

To find which numbers have their decimal expansions non-terminating and  non-repeating.
Each rational integer has a decimal expansion that is either terminating or non-terminating recurring. Note that the three numbers whose decimal expansions are non-terminating and non-recurring:
2 =1.4142… 3 =1.73205… 5 =2.236… 6 =2.828… π=3.14… etc    As a result, the decimal expansions of irrational numbers are non-terminating and non-repeating. Hence, the correct option is 3.
 
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