(- 1 - 984) / |984| × 100% = ? Calculate the Relative Percent Change From Number 984 (Original, Reference) to - 1 (New Value) and the Actual Change (Absolute Difference)

Relative percent change from 984 to - 1

Detailed calculations below

Introduction. Percent, p%

'Percent (%)' means 'out of one hundred':


p% = p 'out of one hundred',


p% is read p 'percent',


p% = p/100 = p ÷ 100.


100% = 100/100 = 100 ÷ 100 = 1.


Relative change. Definition:

Relative change is the difference in an indicator over two periods in time, v2 - v1, 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.


In our case: v1 = 984, v2 = - 1.


Relative change. Formula:

(v2 - v1) / |v1| =


Actual change / |v1|


Legend:


v1 - original number


|v1| - positive value of v1, |v1| >= 0


v2 - new value


Actual change = v2 - v1


/ - fraction bar, division bar:


Actual change / |v1| = Actual change ÷ |v1|


Why using |v1| in the formula, instead of v1?

Calculate the Relative change by using v1 instead of |v1|:

Pick a random negative as original number: - 63.


Pick a random positive as the new value: 79.


Formula:


(79 - (- 63)) / - 63 =


(79 + 63) / - 63 =


142 / - 63


- 2.253968253968 ≈


- 2.25


Though the actual change is positive: 142,


... the relative change is negative: - 2.25. Not good!


By using |v1| instead of v1, the error is corrected.


Note:

Multiply a number by the fraction 100/100,
... and its value doesn't change.


100/100 = 100% = 100 ÷ 100 = 1.


n/100 = n%, any number.


Relative percent change. Formula:

Relative percent change =


Relative change × 100/100 =


(Relative change × 100)/100 =


(Relative change × 100)% =


Calculate the Relative percent change:

(- 1 - 984)/|984| =


- 985/984 =


- 985 ÷ 984 =


- 985 ÷ 984 × 100/100 =


(- 985 × 100 ÷ 984)/100 =


(- 98,500 ÷ 984)/100


- 100.10162601626/100 =


- 100.10162601626% ≈


- 100.1%;


Relative percent change is negative,
so in this case we have a relative percent decrease.


Answer:
:: written in two ways ::

Relative percent change from the original number 984 to the new value of - 1:

Rounded to 12 decimals ≈ - 100.10162601626%
Rounded to maximum 2 decimals ≈ - 100.1%

Actual change:
- 1 - 984 = - 985

Signs: % percent, ÷ divide, × multiply, = equal, / fraction bar (division bar), ≈ approximately equal, |n| - absolute value of n, |n| >= 0;

Writing numbers: comma ',' as thousands separator; point '.' as a decimal mark;

More operations of this kind,
Relative percent change:

From 984 to - 2 = ?


From 984 to 0 = ?


Online calculator: relative percent change

The latest calculated relative percentage changes

Relative percent change from the original number 984 to the new value of - 1 = - 100.10162601626% May 17 14:49 UTC (GMT)
Relative percent change from the original number 1,125 to the new value of 1,205 = 7.111111111111% May 17 14:48 UTC (GMT)
Relative percent change from the original number 246 to the new value of 242 = - 1.626016260163% May 17 14:47 UTC (GMT)
Relative percent change from the original number 56.5 to the new value of 58.28 = 3.150442477876% May 17 14:47 UTC (GMT)
Relative percent change from the original number 1,267 to the new value of 170 = - 86.582478295185% May 17 14:45 UTC (GMT)
Relative percent change from the original number 2,000 to the new value of 997 = - 50.15% May 17 14:45 UTC (GMT)
Relative percent change from the original number 12.6 to the new value of 10.5 = - 16.666666666667% May 17 14:44 UTC (GMT)
Relative percent change from the original number 360 to the new value of 445 = 23.611111111111% May 17 14:43 UTC (GMT)
Relative percent change from the original number 3,690 to the new value of 31,365 = 750% May 17 14:42 UTC (GMT)
Relative percent change from the original number 3.54 to the new value of 3.69 = 4.237288135593% May 17 14:42 UTC (GMT)
Relative percent change from the original number 950 to the new value of 1,045 = 10% May 17 14:41 UTC (GMT)
Relative percent change from the original number 80.78 to the new value of 294.9 = 265.065610299579% May 17 14:35 UTC (GMT)
Relative percent change from the original number 300 to the new value of 885 = 195% May 17 14:29 UTC (GMT)
All the relative percentage changes, calculated by users


>> Calculate the Relative Percentage Decrease


Relative percentage change (relative percentage increase or decrease)

The absolute change (actual difference):

  • The difference between two numerical quantities, y - x, is called absolute difference, actual change or actual difference.
  • When x value is a reference value (the starting value that the value of y is compared to) then the difference between y and x is called the absolute change.
  • The actual difference (actual change) between two values is not always a good way to compare two numbers.
  • The actual change of one unit from number 8 to number 9 is of much more significance than the same difference of one unit between the much larger numbers of 9,999,998 and 9,999,999.
  • In this case we need to take into account the "size" of the quantities involved.

Relative change (from a number x to another number, y):

  • Relative change (from x to y) = (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 so called relative increase.
  • For values y that are smaller than the reference x value, the relative change is negative and in this case we have what it's called a relative decrease.
  • The relative change is not defined if the reference value is zero, x = 0.

Relative percentage change

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

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

  • Relative change (from 2 to 3) = (3 - 2) / |2| = 1/2 = 0.5 = 50%; this change is a relative percentage increase;
  • Relative change (from 9,999,999,998 to 9,999,999,999) = (9,999,999,999 - 9,999,999,998) / |9,999,999,998| = 1/9,999,999,998 ≈ 0 = 0%;
  • Relative change (from 2 to -3) = (-3 - 2) / |2| = -5/2 = -2.5 = -250%; this change is a relative percentage decrease;
  • Relative change (from 9,999,999,998 to -9,999,999,999) = (-9,999,999,999 - 9,999,999,998) / |9,999,999,998| = -19,999,999,997/9,999,999,998 ≈ -2 = -200%; this change is a relative percentage decrease;
  • Relative change (from -2 to 3) = (3 - (-2)) / |-2| = (3 + 2) / 2 = 5/2 = 2.5 = 250%; this change is a relative percentage increase;
  • Relative change (from -9,999,999,998 to 9,999,999,999) = (9,999,999,999 - (-9,999,999,998)) / |-9,999,999,998| = (9,999,999,999 + 9,999,999,998) / 9,999,999,998 = 19,999,999,997/9,999,999,998 ≈ 2 = 200%; this change is a relative percentage increase.

>> Calculate the Relative Percentage Decrease