Pulled up the calculator on my Mac to do a series of small calculations, each of which I could have done in my head, but which in combination were faster with the calculator.
The first... 599.74 times 2.
The correct answer: 1199.48
The answer the calculator application bundled into Mac OS X 10.4 gave: 1,199.48000000000001
Now I've run into this kind of thing before, but only in programming. And usually it's explained away by some nonsense about floating point precision and how the programming language or the microchip's registers treat numbers.
It doesn't seem to be a huge hairy deal from an engineering standpoint. That 0.00000000000001 is a 100,000,000,000,000th, or one one-hundred-trillionth. In a distance of 100 million kilometers (2/3 of the distance between Earth and the sun), it represents a millimeter of deviation.
If you hadn't seen the deviation, if it lay behind the great and powerful wizard's curtain, it's technically so inconsequential as to not change anything in any meaningful way. It's a completely correctable rounding error. But when you see it. When you see an answer get eleven zeroes and a one added that don't belong there, it suddenly becomes VERY meaningful because it's very visibly wrong. It shouldn't be there. And if your computer's doing a simple calculation like that wrong, can you really trust it to balance your checkbook or do your taxes?
It doesn't matter that you'd have to make a trillion dollars a year for it to be off by a penny. It might be off by a billionth of a penny. But knowing that it's off by a billionth of a penny instead of being dead on accurate is somehow unnerving, because your taxes, your bank balance, your medical diagnostic imaging... you want to have 100% confidence in them, not 99.999999999999% confidence in them.
So as much as I could explain it away and tell you why it happens and why it's nothing to worry about... Apple could have fixed it before they released it. And by fixed, I don't mean actually made the calculations perfect. I just mean fixed the decimal display to say 8 or 9 digits of precision, which would hide this little rounding error and make people feel much more confident that Macs won't screw any trillionaires out of a penny come tax season.
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