(1.24 - (- 24)) / |1.24| × 100% = ? Calculate the Relative Percent (Decrease) Change From the Initial (Original, Reference) Value 1.24 to the New One, - 24 (the End Value), and the Actual Change (the Absolute Difference)
The relative percent decrease (change), from 1.24 to - 24
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 = 1.24, v2 = - 24.
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: - 76.
Choose a random positive number for the end value: 18.
Formula and calculation:
(v1 - v2) / v1 =
(- 76 - 18) / - 76 =
-94 / - 76 ≈
1.236842105263 ≈
1.24
Although the absolute change is negative: -94,
... the relative change is positive: 1.24.
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):
(1.24 - (- 24))/|1.24| =
(1.24 + 24)/|1.24| =
25.24/1.24 =
25.24 ÷ 1.24 =
25.24 ÷ 1.24 × 100/100 =
(25.24 × 100 ÷ 1.24)/100 =
(2,524 ÷ 1.24)/100 ≈
2,035.483870967742/100 =
2,035.483870967742% ≈
2,035.48%
(Rounded off to max. 2 decimal places)
The relative percent decrease (change)...
from the initial value 1.24 to the final value - 24:
Rounded off to max. 12 decimal places ≈ 2,035.483870967742%
Rounded off to max. 2 decimal places ≈ 2,035.48%
The actual change
1.24 + 24 = 25.24
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.