(- 10,000 - 312) / |- 10,000| × 100% = ? Calculate the Relative Percent (Decrease) Change From the Initial (Original, Reference) Value - 10,000 to the New One, 312 (the End Value), and the Actual Change (the Absolute Difference)
The relative percent decrease (change), from - 10,000 to 312
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 = - 10,000, v2 = 312.
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: - 23.
Choose a random positive number for the end value: 36.
Formula and calculation:
(v1 - v2) / v1 =
(- 23 - 36) / - 23 =
-59 / - 23 ≈
2.565217391304 ≈
2.57
Although the absolute change is negative: -59,
... the relative change is positive: 2.57.
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):
(- 10,000 - 312)/|- 10,000| =
- 10,312/10,000 =
- 10,312 ÷ 10,000 =
- 10,312 ÷ 10,000 × 100/100 =
(- 10,312 × 100 ÷ 10,000)/100 =
(- 1,031,200 ÷ 10,000)/100 =
- 103.12/100 =
- 103.12%
The relative percent decrease (change)...
from the initial value - 10,000 to the final value 312:
= - 103.12%
The actual change
- 10,000 - (312) = - 10,000 - 312 = - 10,312
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.