Which of the following is an irrational number?

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0.15

0.15 16 ¯

0. 1516 ¯

0.501500150001 ....

answer is D.

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Detailed Solution

We have to identify the irrational number from the given options.
For 0.15, it can be expressed in

\frac{p}{q}

form, so it is a rational number.
i.e. 0.15

= \frac{15}{100}

For

0.15161616...

, the two digits after the decimal that is 16 repeats regularly which means the given number is non-terminating and repeating, so it is a rational number.
For 0.15161516…, the four digits after the decimal that is 1516 repeats regularly which means the given number is non-terminating and repeating, so it is a rational number.
But, 0.501500150001 this is not a terminating and non-repeating number.
Therefore, 0.501500150001 is an irrational number.
Hence, the correct option is 4.

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