To change a repeating decimal to a fraction, express the repeating digits over an equal number of 9s. Then reduce the resulting fraction. I'll show a couple of simple examples, then a couple of harder ones. The repeating digits will be shown with an underscore. (Usually, they are shown with an overbar, but I don't know how to do that on Blurtit.) Pay attention to place value.

__Examples__0.__3__= 3/9 = 1/3 0.142857 = 142857/999999 = (1*142857)/(7*142857) = (1/7)(142857/142857) = 1/7 0.1__6__= (1 6/9)/10 = (1 2/3)/10 = (5/3)/10 = 5/30 = (1*5)/(6*5) = (1/6)(5/5) = 1/6 0.58__3__= (58 3/9)/100 = (58 1/3)/100 = 175/300 = (7*25)/(12*25) = (7/12)(25/25) = 7/12