(79.99 - 4) / |79.99| × 100% = ? Calculate the relative percent (decrease) change from the initial (original, reference) value 79.99 to the new one, 4 (the end value), and the actual change (the absolute difference)
The relative percent decrease (change), from 79.99 to 4
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 = 79.99, v2 = 4.
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: - 43.
Choose a random positive number for the end value: 33.
Formula and calculation:
(v1 - v2) / v1 =
(- 43 - 33) / - 43 =
-76 / - 43 ≈
1.767441860465 ≈
1.77
Although the absolute change is negative: -76,
... the relative change is positive: 1.77.
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):
(79.99 - 4)/|79.99| =
75.99/79.99 =
75.99 ÷ 79.99 =
75.99 ÷ 79.99 × 100/100 =
(75.99 × 100 ÷ 79.99)/100 =
(7,599 ÷ 79.99)/100 ≈
94.999374921865/100 =
94.999374921865% ≈
95%
(Rounded off to a maximum of 2 decimal places)
The relative percent decrease (change)...
from the initial value 79.99 to the final value 4:
Rounded off to a maximum of 12 decimal places ≈ 94.999374921865%
Rounded off to a maximum of 2 decimal places ≈ 95%
The actual change
79.99 - 4 = 75.99
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: