Because we work in a base 10 number system, any denominator that can be expressed as a multiple of 2s 5s and 10s will not be infinite and therefore not repeating. 1/8 is 1/(2*2*2) which is .125. 3/4 is 3/(2*2) which is .75. 27/36 is a tricky one because it's not in simplest form. You can divide the top and bottom by 9 to get 3/4 which we already know is .75. 5/8 is 5/(2*2*2) which is .625. That leaves 7/9. 9 cannot be expressed as a multiple of 2s and 5s ad tens so it must be that one. 7/9 is .777777 repeating.
