For the same reason that if you were to be forced to stay to a certain precision, and to take every step, you'd give 10/3*3 as 9.99999....
Say the precision you had to keep to was 10 digits. After 10/3 you'd have 3.333333333. Then when you multiplied that by 3, you'd have 9.999999999.
Now, since we know that the 3s will go on forever, we know that the 9s will go on forever, and so we know that the answer is really 10. But that's not the deal here, the deal is you apply each step as best you can, and then go on to the next.
As well as numbers that will result in recurring representations, there could be those that could be represented precisely, but not with the number of digits you are using.
Just as 10/3 cannot be represented perfectly in decimal, so 230/100 cannot be represented perfectly in binary.
