Question Video: Identify Whether the Fraction Involving 𝜋 is Rational or Irrational Mathematics • 8th Grade

Video Transcript

Is 𝜋 over three a rational or an irrational number?

We begin by recalling the definition of a rational number. It’s one that can be written in the form 𝑎 over 𝑏 where 𝑎 and 𝑏 are integers. They’re whole numbers. Once we have this definition, we can say that an irrational number is one that’s not rational. In other words, it can’t be written in this form. We’re looking to identify whether 𝜋 divided by three is rational or irrational.

We actually know that 𝜋 is an example of an irrational number. It’s one of the ones we’re most familiar with. So, actually, we need to ask ourselves what happens if we divide an irrational number by an integer? Well, it’s still irrational. There’s no way to write 𝜋 divided by three in the form 𝑎 over 𝑏 where 𝑎 and 𝑏 are both integers. Three is an integer, 𝜋 is not. So this is irrational. 𝜋 divided by three is an irrational number.