Video Transcript
Is 𝜋 a rational or an irrational
number? Option (A) a rational number,
option (B) an irrational number.
In this question, we need to state
whether 𝜋 is a rational or an irrational number. We can begin by recalling that a
rational number is any number that can be written as the quotient of two integers,
where we do not divide by zero. We can also recall that this is
equivalent to saying that they are all of the numbers with either a finite or
repeating decimal expansion. We can also recall that irrational
numbers are the number that are not rational. So they are all of the numbers that
cannot be written as the quotient of two integers.
Equivalently, irrational numbers
are all of the numbers with an infinite nonrepeating decimal expansion. It is beyond the scope of this
video to prove that 𝜋 is irrational. However, it is a well-known fact
that we can state that 𝜋 is irrational. In particular, the decimal
expansion of 𝜋 is infinite and nonrepeating, and 𝜋 cannot be written as the
quotient of two integers. Hence, we can say that the answer
is option (B). 𝜋 is an irrational number.
