Calculate the Relative Percent Change From Number 18,285,189 (Original, Reference) to 19,760,455 (New Value) and the Actual Change (Absolute Difference)

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Relative percentage change (relative percentage increase or decrease)

The absolute change (actual difference):

• The difference between two numerical quantities, y - x, is called absolute difference, actual change or actual difference.
• When x value is a 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 (actual change) between two values is not always a good way to compare two numbers.
• The actual change of one unit from number 8 to 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.

Relative change (from a number x to another number, y):

• Relative change (from x to y) = (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.

Relative percentage change

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

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

• Relative change (from 2 to 3) = (3 - 2) / |2| = 1/2 = 0.5 = 50%; this change is a relative percentage increase;
• 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%;
• Relative change (from 2 to -3) = (-3 - 2) / |2| = -5/2 = -2.5 = -250%; this change is a relative percentage decrease;
• 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 percentage decrease;
• Relative change (from -2 to 3) = (3 - (-2)) / |-2| = (3 + 2) / 2 = 5/2 = 2.5 = 250%; this change is a relative percentage increase;
• 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 percentage increase.