Which of the following is an irrational number?

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

0.15

0.15 16 ¯

0. 1516 ¯

0.501500150001 ....

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th