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For real fun, use Excel:

    =0.1+0.2-0.3        => 0

    =(0.1+0.2-0.3)      => 5.55112E-17

(inspired by http://www.cs.berkeley.edu/~wkahan/Mindless.pdf)

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Oh Excel... I'd love to see that up on the site, mind sending me a pull request? https://github.com/erikwiffin/0.30000000000000004

Tried it in Numbers and they both say 0.0000000000000000555111512312578

EDIT: Numbers is http://www.apple.com/mac/numbers/

LibreOffice Calc shows both as 0.

Try changing the cell to show as many floating points as possible (in Numbers it was to set it to "Automatic").

Sill both zero (dot many zeroes).

I saw the same thing in Numbers until I expanded the field to a larger width, which revealed the non-zero digits at the very end of all the zeroes.

That... is not a known hardware floating point representation. There are way too many digits. This is a just-plain-buggy conversion routine I'm guessing? What is Numbers, and why isn't it using a proper arbitrary precision library if it doesn't want to use doubles?

Edit: sorry, my brain was still reading the leading 0.3 from the linked article. There is indeed nothing wrong with that representation except the nonstandard leading zeroes.

Apple's brand of Excel.

uh, perl gives exactly the same answer as Numbers

> perl -E 'say .1 + .2 - .3'

5.55111512312578e-17

And python actually gives one more digit than Numbers

> python -c 'print(repr(.1 +.2 -.3))'

5.551115123125783e-17

So, I'm not sure why you are claiming "there are way too many digits" and that Numbers is doing something wrong.

What? No, it's a perfectly valid floating point number, represented in a way that lay people might understand.

Those zeros are not part of the mantissa.

A double can hold 15-17 significant base 10 digits. The exponent can be +-10^308 (11 bits for the exponent, 52 bits for the fraction, 1 bit for the sign).

Yes yes yes, I know how to represent an IEEE value. It was an interpretation error: the linked article shows a zillion variants of numbers with a leading significant of 0.3 (i.e. all the leading zeros are significant) while the posted string above did not.

Postgres gives the same response.

# select 0.1::float + 0.2::float - 0.3::float; ---------------------- 5.55111512312578e-17

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