(- 0.07 - 595.3) / |- 0.07| × 100% = ? Calculate the Relative Percent (Decrease) Change From the Initial (Original, Reference) Value - 0.07 to the New One, 595.3 (the End Value), and the Actual Change (the Absolute Difference)
The relative percent decrease (change), from - 0.07 to 595.3
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 = - 0.07, v2 = 595.3.
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: - 22.
Choose a random positive number for the end value: 21.
Formula and calculation:
(v1 - v2) / v1 =
(- 22 - 21) / - 22 =
-43 / - 22 ≈
1.954545454545 ≈
1.95
Although the absolute change is negative: -43,
... the relative change is positive: 1.95.
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):
(- 0.07 - 595.3)/|- 0.07| =
- 595.37/0.07 =
- 595.37 ÷ 0.07 =
- 595.37 ÷ 0.07 × 100/100 =
(- 595.37 × 100 ÷ 0.07)/100 =
(- 59,537 ÷ 0.07)/100 ≈
- 850,528.571428571429/100 =
- 850,528.571428571429% ≈
- 850,528.57%
(Rounded off to max. 2 decimal places)
The relative percent decrease (change)...
from the initial value - 0.07 to the final value 595.3:
Rounded off to max. 12 decimal places ≈ - 850,528.571428571429%
Rounded off to max. 2 decimal places ≈ - 850,528.57%
The actual change
- 0.07 - (595.3) = - 0.07 - 595.3 = - 595.37
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.