Question

Which of the following are irrational numbers?

A. pie (the number lol)
B. 4.8 repeating
C. square root of 9
D. all of the above

Answer 1

A

The definition if a rational number us har it can be written as a ration or as a fraction. Pi is a number that keeps on going and doesnt have
have a specific
pattern unlike B, which has a pattern of 888888888888s (repeating)

Answer 2

`\pi` is the only irrational number on the list. As a reminder, an irrational number is one which can't be written as a ratio of two integers.

With a little scratch work, we can show that
`4.\overline{8}` can be written this way:

`x = 4.\overline{8}\\10x=48.\overline{8}\\10x-x=48.\overline{8}-4.\overline{8}\\9x=44\\x=(44)/(9)`

And
`√(9)=3`, which can be written as a ratio like
`(3)/(1), (6)/(2),(9)/(3)`, or any other where the numerator is 3 times larger than the denominator.

A proof of the irrationality of
`\pi` is pretty involved and advanced, so you'll just have to take my word for it for now!