(- 20 - 527.7) / |- 20| × 100% = ? Calculate the Relative Percent (Decrease) Change From the Initial (Original, Reference) Value - 20 to the New One, 527.7 (the End Value), and the Actual Change (the Absolute Difference)
The relative percent decrease (change), from - 20 to 527.7
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 = - 20, v2 = 527.7.
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: - 4.
Choose a random positive number for the end value: 24.
Formula and calculation:
(v1 - v2) / v1 =
(- 4 - 24) / - 4 =
-28 / - 4 =
7
Although the absolute change is negative: -28,
... the relative change is positive: 7.
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):
(- 20 - 527.7)/|- 20| =
- 547.7/20 =
- 547.7 ÷ 20 =
- 547.7 ÷ 20 × 100/100 =
(- 547.7 × 100 ÷ 20)/100 =
(- 54,770 ÷ 20)/100 =
- 2,738.5/100 =
- 2,738.5%
The relative percent decrease (change)...
from the initial value - 20 to the final value 527.7:
= - 2,738.5%
The actual change
- 20 - (527.7) = - 20 - 527.7 = - 547.7
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.