(7.1 - 5) / |7.1| × 100% = ? Calculate the Relative Percent (Decrease) Change From the Initial (Original, Reference) Value 7.1 to the New One, 5 (the End Value), and the Actual Change (the Absolute Difference)
The relative percent decrease (change), from 7.1 to 5
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 = 7.1, v2 = 5.
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: - 34.
Choose a random positive number for the end value: 94.
Formula and calculation:
(v1 - v2) / v1 =
(- 34 - 94) / - 34 =
-128 / - 34 ≈
3.764705882353 ≈
3.76
Although the absolute change is negative: -128,
... the relative change is positive: 3.76.
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):
(7.1 - 5)/|7.1| =
2.1/7.1 =
2.1 ÷ 7.1 =
2.1 ÷ 7.1 × 100/100 =
(2.1 × 100 ÷ 7.1)/100 =
(210 ÷ 7.1)/100 ≈
29.577464788732/100 =
29.577464788732% ≈
29.58%
(Rounded off to max. 2 decimal places)
The relative percent decrease (change)...
from the initial value 7.1 to the final value 5:
Rounded off to max. 12 decimal places ≈ 29.577464788732%
Rounded off to max. 2 decimal places ≈ 29.58%
The actual change
7.1 - 5 = 2.1
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.