Garbage when using extended numbers

[Bonhomme]

Hi there,
I am writing a LabVIEW VI that requires large decimal numbers. When I use an input value of say 819.2, the value that is actually entered in is something like 819.200012271. Why is this? I need the value to remain at exactly 819.2. Thanks!

[Ben]

"Why"

There is no exact way to represent the ".2" part of the number in binary.

You can do .5 because it is 1/2.
You can do .25 because it is 1/4.

Exact fractions where the denomenator is a power of two can be represented. All others can only be aproximated.

Adding more digits (actually bit) to your number will get you a closer approximation, but never ".2".

Maybe this twisted example will illustrate.
In "trinary" number systems, you can have a value of ".1" base 3. This would be represented as a fraction as 1/3 EXACTLY! This can not be done in decimal, binary or any even numbered number system.

I hope this explains without getting into anything involving the greek alphabet.

Ben