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 = 244, v2 = 268.6.
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: - 18.
- Choose a random positive number for the end value: 60.
Formula and calculation:
(v1 - v2) / v1 =
(- 18 - 60) / - 18 =
-78 / - 18 ≈
4.333333333333 ≈
4.33
Although the absolute difference is negative: -78, the relative decrease change is positive: 4.33. 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:
(244 - 268.6)/|244| =
- 24.6/244 =
- 24.6 ÷ 244 =
- 24.6 ÷ 244 × 100/100 =
(- 24.6 × 100 ÷ 244)/100 =
(- 2,460 ÷ 244)/100 ≈
- 10.081967213115/100 =
- 10.081967213115% ≈
- 10.08%
(Rounded off to max. 2 decimal places)
The relative percent decrease change
from the original, initial value 244 to the final, end value 268.6:
Rounded off to max. 12 decimal places ≈ - 10.081967213115%
Rounded off to max. 2 decimal places ≈ - 10.08%
The absolute (actual) difference
244 - 268.6 = - 24.6
By what percentage has 244 decreased?
Answer: By ≈ - 10.08%
By what percentage is 268.6 smaller than 244?
Answer: By ≈ - 10.08%
The relative percent decrease change is negative,
so in this case we really have a relative percent increase instead
(the value goes up).