(- 0.5 - 461) / |- 0.5| × 100% = ? Calculate the relative percent (decrease) change from the initial (original, reference) value - 0.5 to the new one, 461 (the end value), and the actual change (the absolute difference)
The relative percent decrease (change), from - 0.5 to 461
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 = - 0.5, v2 = 461.
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: - 87.
Choose a random positive number for the end value: 62.
Formula and calculation:
(v1 - v2) / v1 =
(- 87 - 62) / - 87 =
-149 / - 87 ≈
1.712643678161 ≈
1.71
Although the absolute change is negative: -149,
... the relative change is positive: 1.71.
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):
(- 0.5 - 461)/|- 0.5| =
- 461.5/0.5 =
- 461.5 ÷ 0.5 =
- 461.5 ÷ 0.5 × 100/100 =
(- 461.5 × 100 ÷ 0.5)/100 =
(- 46,150 ÷ 0.5)/100 =
- 92,300/100 =
The relative percent decrease (change)...
from the initial value - 0.5 to the final value 461:
= - 92,300%
The actual change
- 0.5 - (461) = - 0.5 - 461 = - 461.5
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.
Other similar operations with percentages: