Steve's Programming Challenge: Weights and Measures

[SMcNeill]

I wrote my program to check all combinations of the above and discovered that the .1 LB could get close, but not exact:

Exactly. And that's the error which we see in floating point math. We can get close to representing some values, but never exact.

That *close but not exact* is the cause of floating point errors that we see when doing math. It's simply impossible to perfectly represent some values in binary-numbers, just as it's impossible to perfectly represent some numbers in standard base-10 values.

What is 1/3 as a decimal?

0.33333333333333333333333333333333333333333333333333333333333(keep holding down that 3 key... you haven't got it perfect yet...)

We can't perfectly represent 1/3 in decimal.

We also can't perfectly represent 1/10 in binary. We get "close, but not exact", and that "close" is where our math errors and rounding errors occur over time in our programs.