185.3 + 12.37 = 197.67000000000002?

Question

This page has a simple alert:

alert(185.3 + 12.37);

To me, that should equal 197.67

However, in the browsers I've tested (Chrome/Safari on OSX, FF on Win7) the answer is:

197.67000000000002

Why is that? Is this just a known bug or is there more to JavaScript addition than I realize?

Welcome to the world of floats. See [Understanding floating point problems](http://stackoverflow.com/questions/4664662/understanding-floating-point-problems) for example. — deceze, Apr 11 '11 at 01:23
Those are numbers that don't have exact binary representations, so it's not at all unusual to get some noise in the low-order bits. — Mike Dunlavey, Apr 11 '11 at 01:25
@Mike...ah! Thanks for that. So it's an issue of our base10 math converting to binary. — DA., Apr 11 '11 at 01:28
@Richard: Actually, floating point is exact, I believe, if you stick to integers, or multiples of 2^n where n can be positive or negative (i.e. 1.75 = 7 * 2^-2). — Mike Dunlavey, Apr 11 '11 at 01:28
Yup, you are correct Mike, that's about the mathematical definition of "in finite places" in this case. 1.75 would be 2^0 + 2^-1 + 2^-2. — Femaref, Apr 11 '11 at 01:32
I'm actually surprised by the number of people that are surprised to see this. — Esteban Araya, Apr 11 '11 at 03:39

score 8 · Accepted Answer · answered Apr 11 '11 at 01:24

8

javascript uses the double datatype, which can't, due to restricted binary places, express all decimal numbers accurately (not all numbers can be expressed with finite binary places). You can read more at wikipedia.

answered Apr 11 '11 at 01:24

Femaref

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Well, it looks like this question has been asked before. ;O) Thanks for the answer! – DA. Apr 11 '11 at 01:28

score 3 · Answer 2 · answered Apr 11 '11 at 01:27

3

You should read this:

http://download.oracle.com/docs/cd/E19957-01/806-3568/ncg_goldberg.html

It's not a bug; it's just a well-known fact of floating point numbers for every language.

answered Apr 11 '11 at 01:27

duffymo

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score 2 · Answer 3 · answered Apr 11 '11 at 01:29

2

In binary, this is the infinitely repeating binary fraction 11000101.10(10101110000101000111) - which cannot be represented in a finite number of bits, so it is rounded to an approximation.

answered Apr 11 '11 at 01:29

Random832

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185.3 + 12.37 = 197.67000000000002?

3 Answers3