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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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