Relative Percent Decrease From Number 50 (Original Value) to 62.3 (End Value)

Calculate the relative percent decrease change from the original value 50 to the end value, 62.3 and the actual change

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 = 50, v2 = 62.3.


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: - 2.

Choose a random positive number for the end value: 84.


Formula and calculation:

(v1 - v2) / v1 =

(- 2 - 84) / - 2 =

-86 / - 2 =

43


Although the absolute change is negative: -86,

... the relative change is positive: 43.

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):

(50 - 62.3)/|50| =

- 12.3/50 =

- 12.3 ÷ 50 =

- 12.3 ÷ 50 × 100/100 =

(- 12.3 × 100 ÷ 50)/100 =

(- 1,230 ÷ 50)/100 =

- 24.6/100 =

- 24.6%

The relative percent decrease (change)...
from the initial value 50 to the final value 62.3:
= - 24.6%

The actual change
50 - 62.3 = - 12.3

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 50 to the end value of 57.8 = ?

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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