Why does 0.1 * 10.0 == 1

Question

In MATLAB the following is true

0.1 * 10.0 == 1

But 0.1 is not represented exactly in floating point, so I expected it to not be true. Did I just get lucky and the error happened to be smaller than eps, so it got rounded to 1?

MATLAB implements IEEE 754, so I think it should apply to all languages. But this post makes me think it might be something specific to MATLAB.

You are probably lucky yes. This post may provide more insight: http://stackoverflow.com/questions/686439/why-is-24-0000-not-equal-to-24-0000-in-matlab — rayryeng, Oct 23 '15 at 17:53
`0.1 + 0.2 + 0.3 - 0.6 = 1.110223024625157e-16` while `0.1 + 0.2 + 0.3 + 0.4 - 1.0 = 0.0` (R2012b) :-) — il_raffa, Oct 23 '15 at 17:59
Try increasing the total number of digits of precision for display: `format long g;`, then go and compute your stuff. On my machine, doing `0.1*10.0` does in fact give me 1, and this is probably because of what you're suspecting. However, doing something like what @il_raffa does you don't see unless you increase the total number of digits. — rayryeng, Oct 23 '15 at 18:19

score 9 · Accepted Answer · edited May 23 '17 at 10:27

Your specific example is true for any language which uses IEEE754 floating point arithmetic (well, 64-bit at least).

The literal 0.1 is exactly

0.1000000000000000055511151231257827021181583404541015625

10.0 is exactly 10

Their product is therefore

1.000000000000000055511151231257827021181583404541015625

The two closest floating point values are:

1.0
1.000000000000000222044604925031308084726333618164062

of which the first is closest, so the result is rounded to that.

(I'm not 100% sure what is going on in that example you link to: I suspect it has to do with C# using higher intermediate precision)

In general, however, this sort of thing isn't true. e.g. 0.51255*1e5 isn't 51255 (though MATLAB may lie when printing, try 0.51255*1e5-51255).

Why does 0.1 * 10.0 == 1

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