Question

Which option is not correct about an irrational number?
$A.\pi \left(\mathrm{3.14159265....}\right),\sqrt{13}$ (3.605551275...), and e (2.7182818.....) are irrational numbers.
$B.\frac{2}{3}=0.6666$ is not an irrational number because the decimal value is recurring (repeating).
C. The decimal expansion is terminating or non-terminating recurring (repeating) in the irrational numbers.
D. Irrational numbers cannot be expressed in the form of a fraction or ratio.

• A. Only C
• B. A, B, and C
• C. A and C
• D. Only B

Answer 1

The correct option is A Only C

Irrational numbers are real numbers that cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio, such as $\frac{p}{q}$, where p and q are integers, $q\ne 0$. Also, the decimal expansion of an irrational number is neither terminating nor repeating.
Check each statement one-by-one.
A. All $\pi \left(\mathrm{3.14159265....}\right),\sqrt{13(\mathrm{3.605551275...}})$, and e(2.7182818.....) decimal expansions are neither terminating nor repeating, it is an irrational number. This statement is correct.
$B.\frac{2}{3}=0.6666$ is expressed in the form of a ratio, so it cannot be an irrational number.
C. This statement is incorrect because the decimal expansion of irrational numbers is non-terminating and non-recurring at any point.
D. The statement that irrational numbers cannot be expressed in the form of a fraction or ratio is also correct.
So, only the statement in option c is correct.