What set (or sets) of numbers does the number 8.121121112… belong to?

My answer~
The number 8.121121112… belongs to the irrational number set, rational numbers, real numbers.

Question

What set (or sets) of numbers does the number 8.121121112… belong to?

My answer~
The number 8.121121112… belongs to the irrational number set, rational numbers, real numbers.

ganeshie8 · Answer

A number is either rational or irrational

it cannot be both

abbycross167 · Answer

oh ok, is it rational?

ganeshie8 · Answer

A rational number has to either terminate or repeat

ganeshie8 · Answer

" … "

means the number goes on forever. it doesn't terminate

ganeshie8 · Answer

look at the number, do you see any repeating pattern ?

abbycross167 · Answer

no sir... so that means it's irrational right?

ganeshie8 · Answer

Yes!

ganeshie8 · Answer

the digits are not repeating, so it is an irrational number

abbycross167 · Answer

Thank you very much!!

ganeshie8 · Answer

yw

abbycross167 · Answer

@ganeshie8 Is there any other number sets it belongs to?

ganeshie8 · Answer

almost all the numbers that you encounter everday are "real" numbers

ganeshie8 · Answer

both rational and irrational numbers belong to the set of real numbers

abbycross167 · Answer

Alright, thanks again!

ganeshie8 · Answer

np