Answer:
\(2\pi\) is an irrational number.
To understand why, let's recall what rational and irrational numbers are:
- Rational numbers are those that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
- Irrational numbers are those that cannot be expressed as the quotient or fraction of two integers.
Now, \(2\pi\) is the product of the rational number \(2\) and the irrational number \(\pi\). Since \(\pi\) is irrational (it cannot be expressed as a fraction of two integers), and any non-zero rational number multiplied by an irrational number results in an irrational number, \(2\pi\) is also irrational.
Therefore, \(2\pi\) is an irrational number.
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