So the answer starts 0. Then you find that 11 goes into 30 two times, with remainder 8. So the answer starts 0.2. Next you find that 11 goes into 80 seven times, with remainder 3. So the answer starts 0.27.
Every fraction produces a recurring decimal.
That is because there are only a finite number of possibilities for the remainder, so eventually you will encounter a remainder you have seen before, and the pattern of digits will continue from that point on. Such decimals are called terminating decimals . Then you can multiply top and bottom by an appropriate number of 2's and 5's to get a power of 10.