## Decrease numbers by percentages of their values and calculate the absolute percentage change (difference)

### How to calculate the new value of a number by decreasing it by percentage of its value and the absolute percentage change (difference)

- Percentage decreased number = Initial value - Absolute percentage change (difference)
- Absolute percentage change (difference) = Percentage decrease % × Initial value
- Percentage decreased number = Initial value - Percentage decrease % × Initial value = (1 - Percentage decrease %) × Initial value
- In conclusion:
#### Percentage decreased number = (1 - Percentage decrease %) × Initial value

#### Initial value =

^{Percentage decreased number}/_{(1 - Percentage decrease %)}#### Absolute percentage change (difference) = Percentage decrease % × Initial value = New value - Initial value

### Examples of calculations on how to decrease a number by percentage of its value and calculate the absolute percentage change:

- If Percentage decrease % = 20%, (1 - Percentage decrease %) = 1 - 20% = 100/100 - 20/100 = 80/100 = 0.8 =>
**Percentage decreased number**= 0.8 × Initial value, and**Initial value**= Percentage decreased number / 0.8;**Absolute percentage change (difference)**= New value - Initial value; - If Percentage decrease % = 5%, (1 - Percentage decrease %) = 1 - 5% = 100/100 - 5/100 = 95/100 = 0.95 =>
**Percentage decreased number**= 0.95 × Initial value, and**Initial value**= Percentage decreased number / 0.95;**Absolute percentage change (difference)**= New value - Initial value; - If Percentage decrease % = 120%, (1 - Percentage decrease %) = 1 - 120% = 100/100 - 120/100 = -20/100 = -0.2 =>
**Percentage decreased number**= -0.2 × Initial value, and**Initial value**= Percentage decreased number / -0.2;**Absolute percentage change (difference)**= New value - Initial value; - If Percentage decrease % = -30%, (1 - Percentage decrease %) = 1 - (-30%) = 1 + 30% = 100/100 + 30/100 = 130/100 = 1.3 =>
**Percentage decreased number**= 1.3 × Initial value, and**Initial value**= Percentage decreased number / 1.3; this is in fact a percentage increase of the initial number;**Absolute percentage change (difference)**= New value - Initial value.