Identify an irrational number among the following number $0.13$ , $0.13 15 ¯$ , $0. 1315 ¯$ , $0.3013001300013 …$ .

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0.13

0.13 15 ¯

0. 1315 ¯

0.3013001300013 …

answer is D.

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Detailed Solution

It is given,

0.13

0.13 15 ¯

0. 1315 ¯

0.3013001300013 …

Understand that

0.13

is an integer or decimal and so, according to the condition of the rational number it is a rational number. Understand that

0.13 15 ¯

is a rational number because it is recurring decimal expansion.
Understand that

0. 1315 ¯

is a rational number because it is recurring decimal expansion.
Understand that the decimal expansion is non-terminating non-recurring in

0.3013001300013 …

and so,

0.3013001300013 …

is an irrational number.
Hence, the correct option is 4.

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