## The relative percent change (the relative percent increase or decrease). The absolute difference (the actual change). The relative change. Examples

### The absolute difference (the actual change):

- The difference between two numerical quantities, y - x, is called
**the absolute difference**,**the actual change**or**the actual difference**. - When y value is the reference value (the starting value that the value of x is compared to) then the difference between y and x is called the
**absolute change**. - The actual difference (the actual change) between two values is not always a good way to compare two numbers.
- The actual change of one unit between the 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.

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

**The 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.^{(The 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.

### The relative percent change

- The relative
**percent**change is the relative change calculated as a percentage; **Relative percent 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**.