is 2 pi a rational number?

Answer 1

No, \( 2\pi \) is not a rational number. A rational number is defined as a number that can be expressed as the quotient of two integers (i.e., in the form \( \frac{p}{q} \) where \( p \) and \( q \) are integers and \( q \neq 0 \)). The number \( \pi \) is known to be an irrational number, meaning it cannot be expressed as a fraction of two integers. Since the product of a non-zero rational number (like 2) and an irrational number (like \( \pi \)) is always irrational, \( 2\pi \) is also irrational.