OSX Calculator error ?
Using 10.4.10 with latest Intel audio fix, I tried a very simple multiplication with Calculator (ver 4.0.5).
101661.15 x 2 =
Instead of displaying 203322.3 calculator is displaying 203322.29999999999
I've tried subsets of the number (ex: 661.15 x 2) and all come back with a result with .3 at the end. It seems only the whole sequence returns the factional result.
Anyone else seen this before? I did a search and nothing came up.
Mac Mini Intel Mac OS X (10.4.10)
The calculator seems to be working with 64 bit binary numbers internally. 101661.15 does not convert exactly to a binary number, so results won't be exact. Normally the rounding hides this. You probably have Precision (View menu) set to 11. If you reduce it you won't see the error. To see what is actually happening, set Precision to 16. Then enter 101661.15 and multiply by 2. You will see the result with more digits, and can see that if rounded to 11 decimal places it will give 203322.29999999999, but rounded to 10, or less, will give 203322.3, which is what you want.
Any calculator that uses binary internally can have this problem with decimal numbers, but some hide it better than others, such as by not displaying results with more precision than the binary conversion of the inputted decimal values.
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I've been having a lot of trouble with accuracy in Microsoft Excel, which I thought was a bug in their software.
I've since tried the same easy formula in Apple's Numbers app and get the same result.
The following formula should give the result of zero (as 9.2x1600 equals 14720)
=((9.21600)-14720)10000000
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It's a small error, but it doesn't show up (which is why I've multiplied by 10000000) until you need the accuracy - especially if you're using automated comparison/error-checking.
There should never be any such error in such a simple and ordinary multiplication of 0.2 of large numbers
I found that the calculator app that is part of the OS also gives me ridiculously long answers, to several decimal points, for simple sums - try typing 9.2 or 9.3 into it and see the readout on the paper-tape window.
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many thanks
manexI noticed this too with the OSX calculator app in 10.5 and 10.6, it behaves differently (and incorrectly IMO) than the old one.
Set the calculator for basic view and bring up the tape. (I'm using Version 4.5.3 (99.2) for this) type this:
102.2 + 99.99 =
and the result is 202.19 (correct).
But in the tape you get this:
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=202.189999999999998
So it seems the tape is using different math than the main window (btw, decimals set to 15).
As far as 'internally using binary', well, this seems to be the case and this is a serious error on the part of the programmer. With a calculator, you should always do decimal arithmetic internally so the result is accurate. <flame> This was drilled into my head in engineering school, it's a rookie mistake.</flame> It's a serious problem and should be corrected.
For what it's worth, the old (<= 10.4) calculator didn't have this problem, and it seems this is only in the tape part and not the main calculator window.
Regards,
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