(38,820.1 - 38,946.3) / |38,820.1| × 100% = ? Calculate the relative percent (decrease) change from the initial (original, reference) value 38,820.1 to the new one, 38,946.3 (the end value), and the actual change (the absolute difference)
The relative percent decrease (change), from 38,820.1 to 38,946.3
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.
Namely:
v1 - is called the reference value (original, initial number);
v2 - is called the new value (the end value).
In our case: v1 = 38,820.1, v2 = 38,946.3.
The relative decrease (change). Formula:
(v1 - v2) / |v1| =
The actual change / |v1|
Legend:
v1 - the original number
|v1| - the positive value of v1, |v1| >= 0
v2 - the new value
The actual change = v1 - v2
/ - the fraction bar (division)
The actual change / |v1| = The actual change ÷ |v1|
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: - 21.
Choose a random positive number for the end value: 39.
Formula and calculation:
(v1 - v2) / v1 =
(- 21 - 39) / - 21 =
-60 / - 21 ≈
2.857142857143 ≈
2.86
Although the absolute change is negative: -60,
... the relative change is positive: 2.86.
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):
(38,820.1 - 38,946.3)/|38,820.1| =
- 126.2/38,820.1 =
- 126.2 ÷ 38,820.1 =
- 126.2 ÷ 38,820.1 × 100/100 =
(- 126.2 × 100 ÷ 38,820.1)/100 =
(- 12,620 ÷ 38,820.1)/100 =
- 0.325089322284/100 =
- 0.325089322284% ≈
- 0.33%
(Rounded off to a maximum of 2 decimal places)
The relative percent decrease (change)...
from the initial value 38,820.1 to the final value 38,946.3:
Not rounded = - 0.325089322284%
Rounded off to a maximum of 2 decimal places ≈ - 0.33%
The actual change
38,820.1 - 38,946.3 = - 126.2
The relative percent decrease (change) is negative...
so in this case we have a relative percent increase.
The symbols used: % percent, ÷ division, × multiplication, = the equal sign, / the fraction bar, ≈ approximately the same, |n| - the positive value of n, |n| >= 0. Writing numbers: comma ',' - as a thousands separator, point '.' as a decimal mark.
Other similar operations with percentages: