(41,905 - 4) / |41,905| × 100% = ? Calculate the Relative Percent (Decrease) Change From the Initial (Original, Reference) Value 41,905 to the New One, 4 (the End Value), and the Actual Change (the Absolute Difference)
The relative percent decrease (change), from 41,905 to 4
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 = 41,905, v2 = 4.
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: - 39.
Choose a random positive number for the end value: 98.
Formula and calculation:
(v1 - v2) / v1 =
(- 39 - 98) / - 39 =
-137 / - 39 ≈
3.512820512821 ≈
3.51
Although the absolute change is negative: -137,
... the relative change is positive: 3.51.
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):
(41,905 - 4)/|41,905| =
41,901/41,905 =
41,901 ÷ 41,905 =
41,901 ÷ 41,905 × 100/100 =
(41,901 × 100 ÷ 41,905)/100 =
(4,190,100 ÷ 41,905)/100 ≈
99.99045459969/100 =
99.99045459969% ≈
99.99%
(Rounded off to max. 2 decimal places)
The relative percent decrease (change)...
from the initial value 41,905 to the final value 4:
Rounded off to max. 12 decimal places ≈ 99.99045459969%
Rounded off to max. 2 decimal places ≈ 99.99%
The actual change
41,905 - 4 = 41,901
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.