(7.62 - 6) / |7.62| × 100% = ? Calculate the relative percent (decrease) change from the initial (original, reference) value 7.62 to the new one, 6 (the end value), and the actual change (the absolute difference)
The relative percent decrease (change), from 7.62 to 6
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 = 7.62, v2 = 6.
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: - 22.
Choose a random positive number for the end value: 94.
Formula and calculation:
(v1 - v2) / v1 =
(- 22 - 94) / - 22 =
-116 / - 22 ≈
5.272727272727 ≈
5.27
Although the absolute change is negative: -116,
... the relative change is positive: 5.27.
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):
(7.62 - 6)/|7.62| =
1.62/7.62 =
1.62 ÷ 7.62 =
1.62 ÷ 7.62 × 100/100 =
(1.62 × 100 ÷ 7.62)/100 =
(162 ÷ 7.62)/100 =
21.259842519685/100 =
21.259842519685% ≈
21.26%
(Rounded off to a maximum of 2 decimal places)
The relative percent decrease (change)...
from the initial value 7.62 to the final value 6:
Not rounded = 21.259842519685%
Rounded off to a maximum of 2 decimal places ≈ 21.26%
The actual change
7.62 - 6 = 1.62
The relative percent decrease (change) is positive...
so we really have a relative percent decrease.
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: