The relative decrease change. Definition:
The relative decrease change is the difference in an indicator over two periods in time, v1 - v2, relative to the value of the indicator in the earlier period, v1.
- Where:
- v1 - is called the reference value (original, initial number);
- v2 - is called the new value (the end value).
- In our case: v1 = 14,709,382, v2 = 60,158,107.9.
The relative decrease change. Formula:
The relative decrease change =
The actual change / |v1|
(v1 - v2) / |v1| =
- Legend:
- v1 - the original number
- |v1| - the positive value of v1, |v1| >= 0. By example: |10| = 10; |-10| = 10.
- v2 - the new value
- The actual change = v1 - v2
- / - the fraction bar (division)
Why do we use |v1| in the formula instead of v1?
- Let's see what happens if we use v1 instead of |v1|:
- Choose a random negative number as the initial value: - 25.
- Choose a random positive number for the end value: 88.
Formula and calculation:
(v1 - v2) / v1 =
(- 25 - 88) / - 25 =
-113 / - 25 =
4.52
Although the absolute difference is negative: -113, the relative decrease change is positive: 4.52. By using |v1| instead of v1, the error is corrected.
The relative percent decrease change. Detailed calculations below
By multiplying a number by the fraction 100/100,
we change only the form of the result, not the result.
- 100/100 = 100% = 100 ÷ 100 = 1.
- n × 100/100 = (n × 100)/100 = (n × 100)%, any number.
The relative percent decrease change. Formula:
The relative percent decrease change =
The relative decrease change × 100/100 =
(The relative decrease change × 100)/100 =
(The relative decrease change × 100)%
Calculate the relative percent decrease change:
(14,709,382 - 60,158,107.9)/|14,709,382| =
- 45,448,725.9/14,709,382 =
- 45,448,725.9 ÷ 14,709,382 =
- 45,448,725.9 ÷ 14,709,382 × 100/100 =
(- 45,448,725.9 × 100 ÷ 14,709,382)/100 =
(- 4,544,872,590 ÷ 14,709,382)/100 ≈
- 308.977806817445/100 =
- 308.977806817445% ≈
- 308.98%
(Rounded off to max. 2 decimal places)
The relative percent decrease change
from the original, initial value 14,709,382 to the final, end value 60,158,107.9:
Rounded off to max. 12 decimal places ≈ - 308.977806817445%
Rounded off to max. 2 decimal places ≈ - 308.98%
The absolute (actual) difference
14,709,382 - 60,158,107.9 = - 45,448,725.9
By what percentage has 14,709,382 decreased?
Answer: By ≈ - 308.98%
By what percentage is 60,158,107.9 smaller than 14,709,382?
Answer: By ≈ - 308.98%
The relative percent decrease change is negative,
so in this case we really have a relative percent increase instead
(the value goes up).