B = (1 - p%) × A = ? Decrease (Decrement, Change) Numbers by Percentages of Their Initial (Original) Values and Calculate the Actual Change (the Absolute Difference, the Variation). How Do You Decrease a Number by a Percentage of Its Value? All the Steps Explained

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

Four examples of calculations below.

• How to decrease a number by percentage of its value
• How to calculate the absolute percentage change:

Example 1:

• 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;

Example 2:

• 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;

Example 3:

• 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;

Example 4:

• 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.