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 = 0.00227999, v2 = - 55.3.
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: - 59.
- Choose a random positive number for the end value: 7.
Formula and calculation:
(v1 - v2) / v1 =
(- 59 - 7) / - 59 =
-66 / - 59 ≈
1.118644067797 ≈
1.12
Although the absolute difference is negative: -66, the relative decrease change is positive: 1.12. 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:
(0.00227999 - (- 55.3))/|0.00227999| =
(0.00227999 + 55.3)/|0.00227999| =
55.30227999/0.00227999 =
55.30227999 ÷ 0.00227999 =
55.30227999 ÷ 0.00227999 × 100/100 =
(55.30227999 × 100 ÷ 0.00227999)/100 =
(5,530.227999 ÷ 0.00227999)/100 ≈
2,425,549.234426466783/100 =
2,425,549.234426466783% ≈
2,425,549.23%
(Rounded off to max. 2 decimal places)
The relative percent decrease change
from the original, initial value 0.00227999 to the final, end value - 55.3:
Rounded off to max. 12 decimal places ≈ 2,425,549.234426466783%
Rounded off to max. 2 decimal places ≈ 2,425,549.23%
The absolute (actual) difference
0.00227999 + 55.3 = 55.30227999 ≈ 55.3
By what percentage has 0.00227999 decreased?
Answer: By ≈ 2,425,549.23%
By what percentage is - 55.3 smaller than 0.00227999?
Answer: By ≈ 2,425,549.23%
The relative percent decrease change is positive,
so we really have a relative percent decrease
(the value goes down).