Which of the following is irrational? `0. 15\ ` (b) `0. 01516` (c) `0. 1516 ` (d) `0. 50150015000015. .`

Explanation

To determine which of the given numbers is irrational, we need to understand the definitions of rational and irrational numbers. A rational number can be expressed as a fraction of two integers (where the denominator is not zero) and has either a terminating or repeating decimal representation. An irrational number, on the other hand, cannot be expressed as a simple fraction and has a non-terminating, non-repeating decimal representation.

Let's analyze each option step by step:

1. **Option (a): `0.15`**
- This number has a decimal representation that terminates after two decimal places.
- Therefore, `0.15` is a rational number.

...