title: Why do round off errors occur?
body: <p>Can anyone explain why round off errors occur in general? Some explanations online have gone over my head on the internet and I was wondering if anyone had an easy to understand explanation. I have run across this problem occasionally when programming and I have always been stumped as to why this would occur in a computer system. One thing I've noticed is that it occurs when certain numbers are evaluated with certain operations (Ex: multiplication, division, etc...).</p>
  
  <p>For example, sometimes a mathematical calculation would return a number such as 14.000000001 or 45.99999999 instead of the expected values (14 and 46)</p>
  
  <p>Could it be that integer overflow is caused by actions of the programming language in use or some underlying factor in computer systems?</p>