Why does 55.0 / 1.1 equal 49.99999999999999?

Question

Possible Duplicate:
Why 6.84 - 3.6 == 3.2399999999999998

And by extension, why does 49.99999999999999 * 1.1 equal 55.0?

I assume this is do to with floating point arithmetic, but am somewhat perplexed as to why this occurs with such a simple sum, and why it is also true for the multiplication case.

Thanks, I did a search but couldn't find any resources on it. — djlumley, Aug 09 '12 at 04:18
Yeah, everybody has the same question but uses different numbers. :) — Greg Hewgill, Aug 09 '12 at 04:30

score 4 · Accepted Answer · answered Aug 09 '12 at 03:59

4

You're correct, it is entirely to do with floating point arithmetic. Many decimal numbers are only representable to a certain accuracy in binary, which is why you see the behaviour here. This isn't restricted to ruby - I'd suggest reading What every computer scientist should know about floating point arithmetic.

answered Aug 09 '12 at 03:59

Yuushi

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Been a while since I've had to look at anything like this so thanks for the link! – djlumley Aug 09 '12 at 04:19

score 3 · Answer 2 · answered Aug 09 '12 at 03:59

3

Your computer works in binary, not in decimal. The number 1.1 cannot be exactly represented in a finite binary representation, so it is necessarily an approximation.

answered Aug 09 '12 at 03:59

Greg Hewgill

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Why does 55.0 / 1.1 equal 49.99999999999999?

2 Answers2