Which of the following fractions would become a repeating decimal?

a. 1/8

b. 3/4

c. 27/36

d. 7/9

e. 5/8

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.