# (35,300 - 28,000) / |28,000| × 100% = ? Calculate the Relative Percent Change From the Number 28,000 (Original, Reference, Initial) to 35,300 (New Value, End Value) and the Actual Change (Absolute Difference)

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## The relative percent change (the relative percent increase or decrease): 1. The absolute difference (the actual change). 2. The relative change. 3. The relative percent change. 4. Examples

### 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.