The non terminating non – recurring decimal number cannot be represented asA. irrational numberB. rational numberC. real numberD. none of these

To solve this question, let's break down the options and understand the concept.

A non-terminating, non-recurring decimal means that the decimal expansion of the number goes on infinitely without repeating a pattern. For example, the number π (pi) is a non-terminating, non-recurring decimal because its decimal expansion goes on forever without any repeating sequence.

Now let's evaluate the options:

A. Irrational number: A number that cannot be expressed as a fraction of two integers is called an irrational number. Non-terminating, non-recurring decimals are a typical representation of irrational numbers. Examples include π and √2. Therefore, this option is correct.

B. Rational number: A rational number is one that can be written as a fraction of two integers. Rational numbers either have a terminating decimal or a recurring (repeating) decimal. Since a non-terminating, non-recurring decimal does not fit this definition, this option is incorrect.

C. Real number: Real numbers include both rational and irrational numbers. Since non-terminating, non-recurring decimals are a subset of real numbers, this option is also incorrect.

D. None of these: This option would suggest that none of the previous options are correct, but we know that option A (irrational number) is correct. Therefore, this option is incorrect.

So, the correct answer is:

A. irrational number