Because you want mixed fractions, the integer portion remains the same. 1) If the decimal part does not repeat, draw a line under the number, put a '1'under the decimal point and put '0' under all numbers: .075 becomes .075 / 1000 then erase the decimal point and any preceding zero’s then reduce to simplest terms (no short cut there). 2) If the decimal repeats the same number such as .77777… take the number that repeats and put it over 9 so .7777… = 7 / 9 then reduce. 3) If a series of numbers repeats over and over, such as .123123123…take the repeating part, 123 in this case, and put it over the same number of 9’s so this becomes 123 / 999 and reduce, 4) If there are numbers after the decimal but before the repeating, such as .578656565… you need to break up the constant part and the repeating, as in this case: .578 and .000656565…. the .578 becomes 578 / 1000 and other part, 000656565… becomes 65 / 99000. The denominator is the same number of 9's as the repeating part and the same number of 0's that preceding the repeating part. Now you have to add the fractions: 578 / 1000 + 65 / 99000. Never said it would be easy.