2.202002000200002...

There is a pattern there so part of me wants to say yes. But there is technically no repeat or termination so a bigger part of me wants to say no.

I am making answer sheets for my students and initially I was going to say no, this is not a rational number due to the fact there is no repeat or termination of the decimal. But looking at the worksheet, it gives no options for the students to label a number as irrational. Just W, I or Q.

Typically the directions for these sheets are very specific, so that got me thinking that this must be a rational number and that the obvious pattern must allow it to be translated into a fraction somehow, but I am not sure how I would do that. I know how to turn repeating and terminating decimals into fractions but not this if it is in fact possible.

I know it is probably a basic question but I'm at a loss here.