^{(x - y)} / _|x| × 100% = ? Calculate the relative percent (decrease) change from the original (reference, initial, x) to a new value (the end value, y) & the absolute change (the actual difference)

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) = ^{(The absolute change from x to y)} / _|x| = ^{(y - x)} / _|x|, where x is the reference value that y is being compared to and |x| is the positive value of 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.

Calculate The Relative Percent Change