in answer to both of your questions regarding the accuracy of numbers, you are apparently working under the mistaken impression that computers work in the decimal number system. They do not. They work in the binary number system which means that while integers can be expressed exactly the same as in decimal, fractions cannot because "rational" numbers are not the same in the two systems. The conversion from decimal to/from binary for fractional numbers cannot be exact, thus producting the differences you see when you convert a number to binary and then back to decimal.