From 10,000 To - 13.9 Relative Percent Decrease (Change, Difference), What Is It?

Calculate the Relative Percent Decrease (Change) From 10,000 to - 13.9 and the Absolute Difference

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 = - 13.9.

The relative decrease (change). Formula:

The relative decrease (change) =

The actual change / |v1|

(v1 - v2) / |v1| =


  • Legend:
  • v1 - the original number
  • |v1| - the positive value of v1, |v1| >= 0. By example: |10| = 10; |-10| = 10.
  • v2 - the new value
  • The actual change = v1 - v2
  • / - the fraction bar (division)

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: - 39.
  • Choose a random positive number for the end value: 74.

Formula and calculation:

(v1 - v2) / v1 =

(- 39 - 74) / - 39 =

-113 / - 39 ≈

2.897435897436 ≈

2.9


Although the absolute difference is negative: -113, the relative decrease (change) is positive: 2.9. 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 - (- 13.9))/|10,000| =

(10,000 + 13.9)/|10,000| =

10,013.9/10,000 =

10,013.9 ÷ 10,000 =

10,013.9 ÷ 10,000 × 100/100 =

(10,013.9 × 100 ÷ 10,000)/100 =

(1,001,390 ÷ 10,000)/100 =

100.139/100 =

100.139% ≈

100.14%
(Rounded off to max. 2 decimal places)

The relative percent decrease (change)
from the original, initial value 10,000 to the final, end value - 13.9:

Not rounded = 100.139%
Rounded off to max. 2 decimal places ≈ 100.14%

The absolute (actual) difference
10,000 + 13.9 = 10,013.9

The relative percent decrease (change) is positive,
so we really have a relative percent decrease
(the value goes down).

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.

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

The absolute difference (the actual variation):

  • 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 decrease (change) from a number x to another number y

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

The relative percent decrease

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

Examples of calculating the relative percent decrease (change)

  • Relative change (from 3 to 2) = (3 - 2) / |3| = 1/3 = 0.33 = 33%
    This change is a relative percentage decrease;
  • Relative decrease (from 9,999,999,999 to 9,999,999,998) = (9,999,999,999 - 9,999,999,998) / |9,999,999,999| = 1/9,999,999,999 ≈ 0 = 0%;
  • Relative decrease (from -3 to 2) = (- 3 - 2) / |-3| = - 5/3 = -1.67 = -167%.
    The relative percent decrease is negative so we have in fact a relative percent increase;
  • The relative percent decrease (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 percent increase;
  • Relative percent decrease (from 3 to -2) = (3 - (-2)) / |3| = (3 + 2) / |3| = 5/3 = 1.67 = 167%
    This change is a relative percentage decrease;
  • Relative decrease (from 9,999,999,999 to - 9,999,999,998) = (9,999,999,998 - (-9,999,999,999)) / |9,999,999,999| = (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 Increase (Change)