Question

Which of the following is an irrational number?

Options

• `3.bar(73)`

• 1.626262......

• 1.323223222.......

• 1.8

Answer 1

1.323223222.......

Explanation:

• An irrational number is a number that cannot be expressed as a fraction of two integers and has a non-terminating, non-repeating decimal expansion.
• Option (a) `3.bar(73)` is a rational number because it is a terminating decimal.
• Option (b) 1.626262...... is a repeating decimal, which is rational.
• Option (c) 1.323223222....... is a non-terminating, non-repeating decimal, indicating it is irrational.
• Option (d) 1.8 is a rational number as it is a terminating decimal.

Hence, 1.323223222....... is an irrational number.