Why 6.84 - 3.6 == 3.2399999999999998

Question

I just encountered this and can't figure out why exactly Ruby behaves this way.

Could someone explain why in Ruby:

6.84 - 3.6 == 3.2399999999999998

and not just 3.24? I know that it's related to the binary representation of those number and that

(Decimal('6.84') - Decimal('3.6'))

would return the expected results. I'm just curious about the detailed explanation of the Float behavior.

The population of Floating Point Town just went up by 0.9999999999834818. — tadman, May 23 '12 at 15:04
possible duplicate of [Why is the 100*0.07 equal to 6.9999....?](http://stackoverflow.com/questions/10711068/why-is-the-1000-07-equal-to-6-9999) — Andrew Marshall, Aug 09 '12 at 04:14
This isn't a Ruby problem, it's a floating-point problem seen in all languages using floating-point. — the Tin Man, Apr 05 '16 at 18:39

score 3 · Answer 1 · edited May 23 '17 at 12:24

3

See the answers in "Why is the 100*0.07 equal to 6.9999....?" (and many other places) about floating-point math.

Why is the 100*0.07 equal to 6.9999....?

edited May 23 '17 at 12:24

Community

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answered May 23 '12 at 14:12

andyras

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score 3 · Answer 2 · answered May 23 '12 at 14:12

3

Because double/float use base-2 notation and decimal base-10 notation.

Here's a useful link: http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

answered May 23 '12 at 14:12

t3hn00b

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Schifty · Answer 3 · 2012-05-23T14:30:25.140

Float/Double is not that precise in most cases (because floats interpolate numbers with base2). The result of floating point operations may vary on different CPU's. The area close to .01 is more precise than the area close to .99

If you need to compare values calculated with float operations use an epsilon value (really small value) in order to erase rounding errors.

Pseudocode:

boolean equals(float x, float y) {
float result = x - y;
if(result*result < epsilon)
  return true;
else 
  false;
}

score 1 · Answer 4 · answered May 23 '12 at 14:32

1

It's a binary floating-point problem.

read this

answered May 23 '12 at 14:32

Pier-Alexandre Bouchard

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score 0 · Answer 5 · answered May 23 '12 at 14:14

0

Base notation-2 and decimal base is used by double and float

answered May 23 '12 at 14:14

Yusuf

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score 0 · Answer 6 · answered May 23 '12 at 14:20

0

0.01 or 0.07 cannot be precisely represented in binary floating-point.

answered May 23 '12 at 14:20

Yusuf

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score 0 · Answer 7 · answered May 23 '12 at 15:06

Floating point uses an internal representation that's inherently imprecise. You should always round down your answers for display purposes:

'%.4f' % (6.84 - 3.6)
# => "3.2400"

Left to its own devices, Ruby, like many other languages, will express floating point numbers to a ridiculous degree of precision.

Why 6.84 - 3.6 == 3.2399999999999998

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