2,888... into a rational number?

2.888888....  =

2 + 8/9  =

26 / 9

  ​ 

OK

Forget about the "2"    we'll append that later

Since we have one repeated "8"....put this over the same number of "9's"  as repeated digits.....since we have one repeated digit....put the 8 over one 9    and we have    8/9

Add back the 2   and we have   2 8/9  =  26 / 9

Another approach

Let x = .8888....

And 10x  = 8.8888....so.....

 10x - x  =  8.8888 - .8888

9x  =  8      divide both sides by  9

x  = 8/9

Add back the 2 and we have   2 + 8/9  =  26/9