Calculate the Relative Percent Change From Number 9.7 (Original, Reference) to 9 (New Value) and the Actual Change (Absolute Difference)

Relative percent change from 9.7 to 9

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 = 9.7, v2 = 9.


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: - 82.


Pick a random positive as the new value: 62.


Formula:


(62 - (- 82)) / - 82 =


(62 + 82) / - 82 =


144 / - 82


- 1.756097560976 ≈


- 1.76


Though the actual change is positive: 144,


... the relative change is negative: - 1.76. 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:

(9 - 9.7)/|9.7| =


- 0.7/9.7 =


- 0.7 ÷ 9.7 =


- 0.7 ÷ 9.7 × 100/100 =


(- 0.7 × 100 ÷ 9.7)/100 =


(- 70 ÷ 9.7)/100


- 7.216494845361/100 =


- 7.216494845361% ≈


- 7.22%;


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 9.7 to the new value of 9:

Rounded to 12 decimals ≈ - 7.216494845361%
Rounded to maximum 2 decimals ≈ - 7.22%

Actual change:
9 - 9.7 = - 0.7

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 9.7 to 8 = ?


From 9.7 to 10 = ?


Online calculator: relative percent change

Latest calculated relative percentage increase changes

Relative percent change from the original number 9.7 to the new value of 9 = - 7.216494845361% Jan 18 11:05 UTC (GMT)
Relative percent change from the original number 1.46 to the new value of 1.5 = 2.739726027397% Jan 18 11:03 UTC (GMT)
Relative percent change from the original number 0.4 to the new value of 306 = 76,400% Jan 18 11:02 UTC (GMT)
Relative percent change from the original number 164,090 to the new value of 163,338 = - 0.458285087452% Jan 18 11:01 UTC (GMT)
Relative percent change from the original number 300 to the new value of 610 = 103.333333333333% Jan 18 11:00 UTC (GMT)
Relative percent change from the original number 300 to the new value of 378 = 26% Jan 18 10:59 UTC (GMT)
Relative percent change from the original number 18,285,189 to the new value of 19,760,455 = 8.068092706069% Jan 18 10:53 UTC (GMT)
Relative percent change from the original number 1.56 to the new value of 1.74 = 11.538461538462% Jan 18 10:53 UTC (GMT)
Relative percent change from the original number 2,136 to the new value of 3,143 = 47.144194756554% Jan 18 10:53 UTC (GMT)
Relative percent change from the original number - 2,333,324 to the new value of 23,325,510 = 1,099.668712960566% Jan 18 10:51 UTC (GMT)
Relative percent change from the original number 8,000 to the new value of 9,724 = 21.55% Jan 18 10:51 UTC (GMT)
Relative percent change from the original number 5.96 to the new value of 23 = 285.906040268456% Jan 18 10:49 UTC (GMT)
Relative percent change from the original number 0.0000000079 to the new value of 23 = 291,139,240,406.329113924051% Jan 18 10:45 UTC (GMT)
All relative percentage increase 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