## Relative percentage change (decrease or increase)

### Absolute change (actual difference):

- The difference between two numerical quantities, y - x, is called
**absolute difference**,**actual change**or**actual difference**. - When y value is a reference value (the starting value that the value x is compared to) then the difference between y and x is called the
**absolute change**. - The actual difference or the actual change between two values is not always a good way to compare two numbers.
- The actual change of one unit between numbers 3 and 2 is of much more significance than the same difference of one unit between the much larger numbers of 9,999,999,999 and 9,999,999,998.
- In this case we need to take into account the "size" of the quantities involved.

### Relative change (increase or decrease) from a number x to another number y

**Relative change (from x to y) =**, where x is the reference value that y is being compared to and |x| is the positive value of x.^{(Absolute change from x to y)}/_{|x|}=^{(y - x)}/_{|x|}- For values y larger than the reference value x, the relative change is a positive number, and in this case we have a
**relative increase**. - For values y that are smaller than the reference x value, the relative change is negative, and in this case we have a
**relative decrease**. - The relative change is not defined if the reference value is zero, y = 0.

### Relative percentage change

- Relative
**percentage**change is the relative change calculated as a percentage; **Relative percentage change = Relative change ×**.^{100}/_{100}= (Relative change × 100)%

### Examples of calculating the relative percentage change (increase or decrease)

- Relative change (from 3 to 2) =
^{(2 - 3)}/_{|3|}=^{-1}/_{3}= -0.33 = -33%; this change is a**relative percentage decrease**; - Relative change (from 9.999.999.999 to 9.999.999.998) =
^{(9.999.999.998 - 9.999.999.999)}/_{|9.999.999.999|}=^{-1}/_{9.999.999.999}≈ 0 = 0%; - Relative change (from -3 to 2) =
(2 - (-3)) / _{|-3|}=(2 + 3) / _{3}=^{5}/_{3}= 1.67 = 167%; this change is a**relative percentage increase**; - Relative change (from -9.999.999.999 to 9.999.999.998) =
^{(9.999.999.998 - (-9.999.999.999))}/_{|-9.999.999.999|}=^{19.999.999.997}/_{9.999.999.999}≈ 2 = 200%; this change is a**relative percentage increase**; - Relative change (from 3 to -2) =
^{(-2 - 3)}/_{|3|}=^{-5}/_{3}= -1.67 = -167%; this change is a**relative percentage decrease**; - Relative change (from 9.999.999.999 to - 9.999.999.998) =
^{(-9.999.999.998 - 9.999.999.999)}/_{|9.999.999.999|}=^{-19.999.999.997}/_{9.999.999.999}≈ -2 = -200%; this change is a**relative percentage decrease**.