Question

Which of the following is an irrational number?

• A. 0.2
• B. \(2\frac{2}{5}\)
• C. 1.212121… …..
• D. \(\sqrt{7}\)

Answer 1

The Correct Option is D

Step 1: Recall the definition of an irrational number.

An irrational number is a number that cannot be expressed as a fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \). Irrational numbers have non-terminating and non-repeating decimal expansions.

Step 2: Analyze each option.

• (1) 0.2: This is a terminating decimal, so it is a rational number.
• (2) \( 2\frac{3}{5} \): This is a mixed fraction, which can be written as \( \frac{13}{5} \). It is a rational number.
• (3) 1212121……: This decimal repeats the pattern "12" indefinitely. Repeating decimals are rational numbers.
• (4) \(\sqrt{7}\) is an irrational number.