How computer does floating point arithmetic?

Question

I have seen long articles explaining how floating point numbers can be stored and how the arithmetic of those numbers is being done, but please briefly explain why when I write

cout << 1.0 / 3.0 <<endl; 

I see 0.333333, but when I write

cout << 1.0 / 3.0 + 1.0 / 3.0 + 1.0 / 3.0 << endl; 

I see 1.

How does the computer do this? Please explain just this simple example. It is enough for me.

Answer 1

Check out the article on "What every computer scientist should know about floating point arithmetic"