## Relative percentage change (increase or decrease)

### Actual change:

The difference between two numerical quantities, x - y, is called the **actual difference**. When y value is a refference value (starting value, the value that x is compared to) then the difference bwetween x and y is called the **actual change**.

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

The actual difference or the actual change between two values is not always a good way to compare two numbers. The actual difference of one unit between numbers 3 and 2 is much more significant than the same actual difference of one unit between the much bigger numbers 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 (x, y)

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

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

- Relative change (3, 2) = (3 - 2) / |2| = 1 / 2 = 0.5 = 50%; this is a relative (percentage) increase change
- Relative change (9.999.999.999, 9.999.999.998) = (9.999.999.999 - 9.999.999.998) / |9.999.999.998| = 1 / 9.999.999.998 ~ 0 ~ 0%
- Relative change (-3, 2) = (-3 - 2) / |2| = -5 / 2 = -2.5 = -250%; this is a relative (percentage) decrease change
- Relative change (-9.999.999.999, 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 is a relative (percentage) decrease change
- Relative change (3, -2) = (3 - (-2)) / |-2| = (3 + 2) / 2 = 5 / 2 = 2.5 = 250%; this is a relative (percentage) increase change
- Relative change (9.999.999.999, -9.999.999.998) = (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 is a relative (percentage) increase change