Decimal vs float

float與decimal的區別
Decimal versus Float Point Type
rails中的Float/Decimal數據類型
The primary use for DECIMAL is money, where floating point would fail
miserably and produce lots of errors (money leak) at the end of the month.

As floating point arithmetic has it's own separated section on your
processor (unless you have a 386 or older computer) it would be *much*
faster than DECIMAL, so use it only if you are absolutely sure you need it.

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The difference is that, for example, .01 can be represented exactly in
decimal; but float types are binary, so .01 cannot be represented exactly.
This can lead to all kinds of trouble when doing arithmetic, the errors
accumulate. It's one reason why most people write their loops with "< x + 1"
rather than "= x". That gets past the problem, but if you are adding
together many values the final answer may be wrong.

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myslq> create table numbers (a decimal(10,2), b float);
myslq> insert into numbers values (100, 100);
mysql> select @a := (a/3), @b := (b/3), @a * 3, @b * 3 from numbers \G
*************************** 1. row ***************************
@a := (a/3): 33.333333333
@b := (b/3): 33.333333333333
@a + @a + @a: 99.999999999000000000000000000000
@b + @b + @b: 100

The decimal did exactly what's supposed to do on this cases, it
truncated the rest, thus loosing the 1/3 part.

So for sums the decimal is better, but for divisions the float is
better, up to some point, of course. I mean, using DECIMAL will not give
you a "fail proof arithmetic" in any means.

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How do you expect to split a dollar 3 ways?
It is not the math you do that determins whether you use float or
decimal, it is what you are modeling that is important.
Dollars are decimal, and dollar calculations must be rounded to the
nearest cent, or mill.

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