If you mean 0.26666666.... with the 6's recurring, then do the following:

 

Let  x = 0.266666....

Mutiply x by 100:

100x = 26.666666.....

Multiply x by 10:

10x = 2.666666.....

 

Subtract 10x from 100x:

100x - 10x = 26.66666.... - 2.66666..... so

90x = 24

 

Divide by 90

x = 24/90

or x = 4/15

.

 

On the other hand, if you mean 0.266266266... then

Let x = 0.266266266...

 

Multiply by 1000

1000x = 266.266266266....

 

Subtract x from 1000x

1000x - x = 266.266266266... - 0.266266266...

999x = 266

x = 266/999

.

 266/1000 is 0.266 reoccurring as a fraction?