Why does 1.4 - 0.5 result in 0.8999999999999 999?

[Fredrik Celin]

I use IE 6.0 and does some calculations in a javascript.

If I run this code:
alert(1.4 - 0.5);

i get the result 0.8999999999 and not 0.9
Does anybody know why? Is this a bug in IE or what? Any fast and easy
ways to work around this problem?

B.R
The Duke

[Lasse Reichstein Nielsen]

Grant Wagner <gw*****@agrico reunited.com> writes:

Which is why I wrote "one-third" and "two-thirds", and not 1/3 and
2/3. My example was to show the same errors he accuses computers of
making because they "don't compute" can occur when humans do the
math: 1 + 2 = 3, 3/3 = 1; but 0.333... + 0.666... != 1.
Ok, I didn't say anything the first time, but now I can't keep myself
from nitpicking any more :)

0.333... + 0.666... = 0.999... = 1

That is, if the "..." means an infinite repeating sequence of decimals.
It has to do with how values are represented. A ratio of one over
three _exactly_ represents the value with nothing repeating or being
an approximation, whereas the decimal value
(decimal *representation *)
of 1 divided by 3 can only be an approximation and does not exactly
represent the value of the ratio (and never can).
Yep.
In the same way, some values stored in decimal can exactly represent
a value (0.3 or 0.2), but when that same value is stored in binary,
it can only be stored as an approximation.
Yes. The problem is not the the base of the representation, but the
finiteness of it. While 0.3 has a finite representation in base 10, it
doesn't in base 2. Just as 1/3 doesn't have a finite representation in
base 10, but does in base 3 ("0.1").
I can exactly store a value represented as "2 x sqrt(2)", but the
resulting value would most likely be an approximation in both
decimal and binary. In fact, with imaginary numbers, you can exactly
represent values which you can not even approximate in decimal (or
binary).
Are you sure you mean *imaginary* numbers (because you sure can make
decimal/binary representations of some of those, usually as pairs of
numbers).

We can represent all integers precisely and finitely in a positional
number system with any integer base larger than 1 (although there is
no upper bound on the sizes of the representations , each one of them
is finite).

We can also represent all rational numbers precisely and finitely. The
representation can be a pair of integers. However, we cannot represent
all rational numbers finitly in a single positional number system, no
matter what base (>=2).

We cannot represent all real numbers finitly with a finite alphabet,
no matter how we allow definitions to be written (including arbitrary
prose prose with a one-billion letter alphabet).

Whoa... better get back on track.
The OP was directed to the FAQ, I was responding to someone who had
responded to the OP with a flippant "computers don't compute and
that's why numbers don't get calculated right" remark.

Thanks for answering that. I'm not sure I could ... coherently. :)

/L
--
Lasse Reichstein Nielsen - lr*@hotpop.com
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