Final answer:
To find a number that produces a rational number when added to 0.42, option b, 0.2645751311..., is the correct answer.
Step-by-step explanation:
To find a number that produces a rational number when added to 0.42, we need to consider that a rational number is a number that can be expressed as a fraction of two integers. So, we need to find a number that, when added to 0.42, results in a fraction. Option c, √3, is an irrational number and cannot be expressed as a fraction, so it does not produce a rational number when added to 0.42. Option d, √3, is the same as option c, so it is also incorrect.
The correct answer is either option a or b, since they are the same number. Option a, 0.2645751311..., is an irrational number and cannot be expressed as a fraction. Therefore, the correct answer is option b, 0.2645751311..., which is a rational number and produces a rational number when added to 0.42.