If -3 is change to -3.3, what

My two cents worth. If there is a debt of 3 units and now the new debt becomes 3.3
units, this is a 10% INCREASE in debt. Mathematically, you can write this change as from -3 to -3.3. Similarly, if there is a profit of 3 units and now it becomes 3.3 units, this is also a 10% INCREASE in profit. This means that the % increase or %decrease applying on the base value should follow the ‘direction’ or the sign of the base value.

If you need more examples, you can take vector, which is also directional, as example. If you run in the direction to the West and you increase your speed by 10%, you will never question yourself why you are not moving to the East. In summary, the percentage increase or decrease refers to a change. It is neutral in itself. It’s the direction or the sign of the base value that matters. E.g. 10% increase of -3 is -3 * 10% = -0.3. The increase means adding -0.3 to -3 which gives -3.3. Hope this helps.

How about changing the formula into
(New - |Old|) / |Old| × 100%?

2014-02-16 11:07:38 補充：
批卷貓, what I mean is when both old and new values are negative,

How about changing the formula into
(New - |Old|) / |Old| × 100%?

我不知道大家是否留意清楚。

其實這是一個很有意義的題目，發問者則留意到，故作出此有意義的發問。

如果想避免麻煩，其中一個方法是用以下百分比改變的公式：

　(New - Old) / |Old| × 100%

以 absolute value 作分母。

由於分子已經清楚交代改變，所以發問者的疑難可以解決。

2014-02-15 20:02:30 補充：
但以上的方法也有它的問題。

舉例看以下：

由 -6 變成 3，百分比改變為 [ 3 - (-6) ] / |-6| × 100% = 150%

由 0.5 變成 3，百分比改變為 [ 3 - 0.5 ] / |0.5| × 100% = 500%

但明顯地由 -6 變成 3的增幅應更大，所以以上的方法也有其問題。

所以有人說百分比改變只適用於原數是正數的情況．．．

2014-02-15 20:04:01 補充：
給大家一些有用的參考資料看看：

http://www.mrexcel.com/forum/excel-questions/212975-percent-change-negative-numbers.html

http://leetm.mingpao.com/cfm/Forum3.cfm?CategoryID=1&TopicID=1216&TopicOrder=Desc&TopicPage=23

http://mathforum.org/library/drmath/view/55720.html

2014-02-15 20:04:08 補充：
http://education.blurtit.com/201088/how-do-you-calculate-percentage-when-one-number-is-a-negative-number-if-i-want-to-show

2014-02-15 22:25:40 補充：
See Lok Bay, I am sorry, but this is definitely NOT OK.

This is because changing from -1 to 3 and clearly different from changing from 1 to 3.

The former is an increment of 4 while the latter is just an increment of 2.

2014-02-16 19:42:30 補充：
When both old and new values are negative, for example, let's say changing from -2 to -4.

Then, using your formula:
(-4 - |-2|)/|-2| × 100%
= -6 / 2 × 100%
= -300%

Just looking at the numerator of -6, we can know that is does not make sense.

Therefore, I think your formula is not ok.

I believe that you can easily calculate the % change:
[ (-3.3) - (-3) ] / (-3) = 10%

But then why is the % change a +ve number?

First, we should think what a '% change' is.
e.g.
If a number x has a +ve % change of 50%,
then it's new value should be x(1+50%) = 1.5x
Change= 1.5x - x = 0.5x

That is, the amount of change DEPENDS on the original value.

If there is a number y where y>x and it also has a +ve change of 50%,
then it's new value will be 1.5y
Change= 1.5y - y = 0.5y and obviously the 0.5y>0.5x

Hence the exactly amount of change of y is GREATER than that of x.

That is, the amount of change is dependent of the original value.

Therefore, if the original value is -ve, when it has a +ve % change, it actually decreases in value.
Let say -1,
when it has a +ve % change of 50%,
its new value will be -1(1+50%) = -1.5

The new value -1.5 is smaller than -1
But still it is a +ve % change.

% change only gives us a relative comparison.
2 numbers can have the same % change but the exact amount of change can be different.

A +ve % change does not necessarily mean that the new value is greater than the original one.

因為是說一個改變，改變了多少，-3至-3.3，它變了10%。

The percentage change
=((-3.3)-(-3.))/(-3)*100%
=0.3/3*100%
=10%

2014-02-20 21:01:53 補充：
It is because the base is a negative number.
positive number times a negative number,the result would still be negative number
如果倒轉黎計，
-3*(1+10%)=-3.3

就好似如果話-3大左一倍，既the percentage change=+100%，find the new number，
個答案會係-6，唔會係-3+3=0囉