(- 0.5 - 361.2) / |- 0.5| × 100% = ? Calculate the Relative Percent (Decrease) Change From the Initial (Original, Reference) Value - 0.5 to the New One, 361.2 (the End Value), and the Actual Change (the Absolute Difference)

The relative percent decrease (change), from - 0.5 to 361.2

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 = 361.2.


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: - 37.

Choose a random positive number for the end value: 49.


Formula and calculation:

(v1 - v2) / v1 =

(- 37 - 49) / - 37 =

-86 / - 37 ≈

2.324324324324 ≈

2.32


Although the absolute change is negative: -86,

... the relative change is positive: 2.32.

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 - 361.2)/|- 0.5| =

- 361.7/0.5 =

- 361.7 ÷ 0.5 =

- 361.7 ÷ 0.5 × 100/100 =

(- 361.7 × 100 ÷ 0.5)/100 =

(- 36,170 ÷ 0.5)/100 =

- 72,340/100 =

- 72,340%

The relative percent decrease (change)...
from the initial value - 0.5 to the final value 361.2:
= - 72,340%

The actual change
- 0.5 - (361.2) = - 0.5 - 361.2 = - 361.7

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.


» The relative percent decrease (change) from the original value of - 0.5 to the end value of 361.5 = ?

» New: All the Relative Percentage Decrease (Change) Calculations Performed by Our Visitors - Organized on a Monthly Basis



The relative percent change (the relative percent increase or decrease). The absolute difference (the actual change). The relative change. Examples

The absolute difference (the actual change):

  • The difference between two numerical quantities, y - x, is called the absolute difference, the actual change or the actual difference.
  • When y value is the reference value (the starting value that the value of x is compared to) then the difference between y and x is called the absolute change.
  • The actual difference (the actual change) between two values is not always a good way to compare two numbers.
  • The actual change of one unit between the numbers 3 and 2 is of much more significance than the same difference of one unit between the much larger numbers of 9,999,999,999 and 9,999,999,998.
  • In this case we need to take into account the "size" of the quantities involved.

The relative change (increase or decrease) from a number x to another number y

  • The relative change (from x to y) = (The absolute change from x to y) / |x| = (y - x) / |x|, where x is the reference value that y is being compared to and |x| is the positive value of x.
  • For values y larger than the reference value x, the relative change is a positive number, and in this case we have a relative increase.
  • For values y that are smaller than the reference x value, the relative change is negative, and in this case we have a relative decrease.
  • The relative change is not defined if the reference value is zero, y = 0.

The relative percent change

  • The relative percent change is the relative change calculated as a percentage;
  • Relative percent change = Relative change × 100/100 = (Relative change × 100)%.

Examples of calculating the relative percentage change (increase or decrease)

  • Relative change (from 3 to 2) = (2 - 3) / |3| = -1/3 = -0.33 = -33%
    This change is a relative percentage decrease;
  • Relative change (from 9,999,999,999 to 9,999,999,998) = (9,999,999,998 - 9,999,999,999) / |9,999,999,999| = -1/9,999,999,999 ≈ 0 = 0%;
  • Relative change (from -3 to 2) = (2 - (-3)) / |-3| = (2 + 3) / 3 = 5/3 = 1.67 = 167%
    This change is a relative percentage increase;
  • Relative change (from -9,999,999,999 to 9,999,999,998) = (9,999,999,998 - (-9,999,999,999)) / |-9,999,999,999| = 19,999,999,997/9,999,999,999 ≈ 2 = 200%
    This change is a relative percentage increase;
  • Relative change (from 3 to -2) = (-2 - 3) / |3| = -5/3 = -1.67 = -167%
    This change is a relative percentage decrease;
  • Relative change (from 9,999,999,999 to - 9,999,999,998) = (-9,999,999,998 - 9,999,999,999) / |9,999,999,999| = -19,999,999,997/9,999,999,999 ≈ -2 = -200%
    This change is a relative percentage decrease.

» Calculate The Relative Percent Change