Question

Consider the following three statements.
Statement–1: A number whose decimal expansion is terminating is a rational number.
Statement–2: A number whose decimal expansion is non– terminating recurring is a rational number.
Statement–3: A number whose decimal expansion is terminating non recurring is irrational number.
Which of the following is true?

• A. Statement 1 is true but 2 and 3 are false.
• B. Statement 1 and 2 are false; 3 is true.
• C. Statement 1 and 2 are true; 3 is false.
• D. Statement 1 is false; 2 and 3 are true.

Answer 1

The correct option is C

Statement 1 and 2 are true; 3 is false.

Let's verify the statements one by one.

Statement–1: A number whose decimal expansion is terminating is a rational number.

This statement is true because we know a rational number is either terminating or non-terminating recurring decimal expansion.

For example $0.512=\frac{512}{1000}$ is a rational number.

Statement–2: A number whose decimal expansion is non– terminating recurring is a rational number.

This statement is true because we know a rational number is either terminating or non-terminating recurring decimal expansion.

For example $0.\overline{7}=\frac{7}{9}$ is a rational number.

Statement–3: A number whose decimal expansion is terminating non recurring is irrational number.

This statement is false because we know an irrational number is non-terminating and non-recurring.

For example $\mathrm{\pi }=3.1415....$ is an irrational number.

Hence, statements 1 and 2 are true; 3 is false.

Hence, option C is correct.