SQL Server makes up extra precision for floats?

Question

Precision loss is one thing, but precision gain???

I have a text file w/ the following coordinates:

41.88694340165634   -87.60841369628906

When I paste this into SQL Server Mgmt Studio table view, it results in this:

41.886943401656339  -87.608413696289062

Am I dreaming? How is this possible?

I'm pasting from notepad, and it's raw text. Same problem if I type the characters directly.

Where does sql server get the extra precision from?

Answer 1

It's not adding precision, it's just rounding it to the nearest IEEE floating point representation. When you convert that back to decimal, it only LOOKS like it gained precision.