(- 1 - 13.5) / |- 1| × 100% = ? Calculate the Relative Percent (Decrease) Change From the Initial (Original, Reference) Value - 1 to the New One, 13.5 (the End Value), and the Actual Change (the Absolute Difference)
The relative percent decrease (change), from - 1 to 13.5
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 = - 1, v2 = 13.5.
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: - 97.
Choose a random positive number for the end value: 1.
Formula and calculation:
(v1 - v2) / v1 =
(- 97 - 1) / - 97 =
-98 / - 97 ≈
1.010309278351 ≈
1.01
Although the absolute change is negative: -98,
... the relative change is positive: 1.01.
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 - 13.5)/|- 1| =
- 14.5/1 =
- 14.5 ÷ 1 =
- 14.5 ÷ 1 × 100/100 =
(- 14.5 × 100 ÷ 1)/100 =
(- 1,450 ÷ 1)/100 =
- 1,450/100 =
- 1,450%
The relative percent decrease (change)...
from the initial value - 1 to the final value 13.5:
= - 1,450%
The actual change
- 1 - (13.5) = - 1 - 13.5 = - 14.5
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.