double and accuracy

Question

Using long double I get 18/19 = 0.947368421052631578..., and 947368421052631578 is the repeating decimal. Using double I

Answer 1

You're trying to represent every decimal number with a finite amount of bits. Some things just aren't expressible exactly in floating point. Expecting exact answers with floats is your first problem. Take a look at What Every Computer Scientist Should Know About Floating-Point Arithmetic

Here's a summary from some lecture notes:

As mentioned earlier, computers cannot represent real numbers precisely since there are only a finite number of bits for storing a real number. Therefore, any number that has infinite number of digits such as 1/3, the square root of 2 and PI cannot be represented completely. Moreover, even a number of finite number of digits cannot be represented precisely because of the way of encoding real numbers.