(2,000 - 0) / |2,000| × 100% = ? Calculate the relative percent (decrease) change from the initial (original, reference) value 2,000 to the new one, 0 (the end value), and the actual change (the absolute difference)
The relative percent decrease (change), from 2,000 to 0
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 = 2,000, v2 = 0.
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: - 31.
Choose a random positive number for the end value: 12.
Formula and calculation:
(v1 - v2) / v1 =
(- 31 - 12) / - 31 =
-43 / - 31 ≈
1.387096774194 ≈
1.39
Although the absolute change is negative: -43,
... the relative change is positive: 1.39.
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):
(2,000 - 0)/|2,000| =
2,000/2,000 =
2,000 ÷ 2,000 =
2,000 ÷ 2,000 × 100/100 =
(2,000 × 100 ÷ 2,000)/100 =
(200,000 ÷ 2,000)/100 =
100/100 =
The relative percent decrease (change)...
from the initial value 2,000 to the final value 0:
= 100%
The actual change
2,000 - 0 = 2,000
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.
Other similar operations with percentages: