## Relative percentage change (relative percentage increase or decrease)

### The absolute change (actual difference):

- The difference between two numerical quantities, y - x, is called
**absolute difference**,**actual change**or**actual difference**. - When x value is a reference value (the starting value that the value of y is compared to) then the difference between y and x is called the
**absolute change**. - The actual difference (actual change) between two values is not always a good way to compare two numbers.
- The actual change of one unit from number 8 to number 9 is of much more significance than the same difference of one unit between the much larger numbers of 9,999,998 and 9,999,999.
- In this case we need to take into account the "size" of the quantities involved.

### Relative change (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 so called
**relative increase**. - For values y that are smaller than the reference x value, the relative change is negative and in this case we have what it's called a
**relative decrease**. - The relative change is not defined if the reference value is zero, x = 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 2 to 3) =
^{(3 - 2)}/_{|2|}=^{1}/_{2}= 0.5 = 50%; this change is a**relative percentage increase**; - Relative change (from 9,999,999,998 to 9,999,999,999) =
^{(9,999,999,999 - 9,999,999,998)}/_{|9,999,999,998|}=^{1}/_{9,999,999,998}≈ 0 = 0%; - Relative change (from 2 to -3) =
^{(-3 - 2)}/_{|2|}=^{-5}/_{2}= -2.5 = -250%; this change is a**relative percentage decrease**; - Relative change (from 9,999,999,998 to -9,999,999,999) =
^{(-9,999,999,999 - 9,999,999,998)}/_{|9,999,999,998|}=^{-19,999,999,997}/_{9,999,999,998}≈ -2 = -200%; this change is a**relative percentage decrease**; - Relative change (from -2 to 3) =
^{(3 - (-2))}/_{|-2|}=^{(3 + 2)}/_{2}=^{5}/_{2}= 2.5 = 250%; this change is a**relative percentage increase**; - Relative change (from -9,999,999,998 to 9,999,999,999) =
^{(9,999,999,999 - (-9,999,999,998))}/_{|-9,999,999,998|}=^{(9,999,999,999 + 9,999,999,998)}/_{9,999,999,998}=^{19,999,999,997}/_{9,999,999,998}≈ 2 = 200%; this change is a**relative percentage increase**.