^{(y - x)} / _|x| × 100% = ? Calculate the Relative Percent Change Between Two Numbers & the Actual Change (the Absolute Difference). Is the Change From the Original (Initial, Reference, x) to the New Value (the End Value, y) an Increase or a Decrease (Number Goes Up or Down)?

1. 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 x value is the 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 (the actual change) between two values is not always a good way to compare two numbers.
• The actual change of one unit from the number 8 to the 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.

2. The relative change (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 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.

3. The relative percent change

• The relative percent change is the Relative change calculated as a percentage;
• The relative percent change = The relative change × ¹⁰⁰/₁₀₀ = (The relative change × 100)%.

4. Examples of calculating the relative percent change (increase or decrease)

• The relative change (from 2 to 3) = ^{(3 - 2)} / _|2| = ¹/₂ = 0.5 = 50%
  This change is a relative percent increase.
• The 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%;
• The relative change (from 2 to -3) = ^{(-3 - 2)} / _|2| = ^-5/₂ = -2.5 = -250%
  This change is a relative percent decrease.
• The 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 percent decrease.
• The relative change (from -2 to 3) = ^{(3 - (-2))} / _|-2| = ^{(3 + 2)} / ₂ = ⁵/₂ = 2.5 = 250%
  This change is a relative percent increase.
• The 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 percent increase.

Calculate the Relative Percent Decrease (Change)