(513.2 - 0.0000000001) / |0.0000000001| × 100% = ? Calculate the Relative Percent Change From the Number 0.0000000001 (Original, Reference, Initial) to 513.2 (New, End Value) and the Actual Change (Absolute Difference, Variation). Is the Change an Increase or a Decrease in Value (Number Goes Up or Down)? How Do You Find the Relative Percent Change and the Actual Change?
The relative percent change, from 0.0000000001 to 513.2
(513.2 - 0.0000000001) / |0.0000000001| × 100% = ?
Introduction. Definitions and Formulas. The Relative Percent Change Calculation. The Answer
Introduction. Definitions and formulas
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.
The relative change. Definition:
The 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.
The relative change. Formula:
(v2 - v1) / |v1| =
The actual change / |v1|
Legend:
v2 - is the new value (the end value)
v1 - is the reference value (original, initial number)
In our case: v1 = 0.0000000001, v2 = 513.2.
/ - the fraction bar (division)
|v1| - the positive value of v1, |v1| >= 0
Example: if v1 = -10, |v1| = 10
The actual change = v2 - 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, v1: - 100.
Choose a random positive number for the end value, v2: 43.
Formula and calculation:
(v2 - v1) / v1 =
(43 - (- 100)) / - 100 =
(43 + 100) / - 100 =
143 / - 100 =
- 1.43
Although the absolute change is positive 143
... the relative change is negative: - 1.43.
This is not good!
By using |v1| instead of v1, the error is corrected.
Detailed calculations below
A quick note:
Multiply a number by the fraction 100/100,
... and its value doesn't change.
100/100 = 100% = 100 ÷ 100 = 1.
By multiplying a number by the fraction 100/100,
we change only the form of the result, not the result.
n/100 = n%, any number.
The relative percent change. Formula:
The relative percent change =
The relative change × 100/100 =
(The relative change × 100)/100 =
(The relative change × 100)%
Calculate the relative percent change:
(513.2 - 0.0000000001)/|0.0000000001| =
513.1999999999/0.0000000001 =
513.1999999999 ÷ 0.0000000001 =
513.1999999999 ÷ 0.0000000001 × 100/100 =
(513.1999999999 × 100 ÷ 0.0000000001)/100 =
(51,319.99999999 ÷ 0.0000000001)/100 =
513,199,999,999,900/100 =
513,199,999,999,900%
The answer (scroll down)...
The relative percent change...
from the initial value 0.0000000001 to the final value 513.2:
= 513,199,999,999,900%
The actual change
513.2 - 0.0000000001 = 513.1999999999 ≈ 513.2
The relative percent change is positive...
so in this case we have a relative percent increase.
(the number's value goes up)
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.
Other similar operations with percentages:
Online calculator: Relative Percent Change
The latest 7 calculated relative percentage changes
| Calculate the relative percent change (increase or decrease) from the original (the reference, the initial) value of 0.0000000001 to the final (the new, the end) value of 513.2 = 513,199,999,999,900%. Also calculate the Actual Change (Absolute Difference, Variation) | Sep 23 16:43 UTC (GMT) |
| Calculate the relative percent change (increase or decrease) from the original (the reference, the initial) value of 2,923,335 to the final (the new, the end) value of 3,218,639.1 = 10.101616817778%. Also calculate the Actual Change (Absolute Difference, Variation) | Sep 23 16:41 UTC (GMT) |
| Calculate the relative percent change (increase or decrease) from the original (the reference, the initial) value of 0.0000000001 to the final (the new, the end) value of 142.9 = 142,899,999,999,900%. Also calculate the Actual Change (Absolute Difference, Variation) | Sep 23 16:41 UTC (GMT) |
| Calculate the relative percent change (increase or decrease) from the original (the reference, the initial) value of 25 to the final (the new, the end) value of 10.4 = - 58.4%. Also calculate the Actual Change (Absolute Difference, Variation) | Sep 23 16:41 UTC (GMT) |
| Calculate the relative percent change (increase or decrease) from the original (the reference, the initial) value of 0.94 to the final (the new, the end) value of 0.64 = - 31.914893617021%. Also calculate the Actual Change (Absolute Difference, Variation) | Sep 23 16:40 UTC (GMT) |
| Calculate the relative percent change (increase or decrease) from the original (the reference, the initial) value of 100 to the final (the new, the end) value of 101.4 = 1.4%. Also calculate the Actual Change (Absolute Difference, Variation) | Sep 23 16:40 UTC (GMT) |
| Calculate the relative percent change (increase or decrease) from the original (the reference, the initial) value of 4,046 to the final (the new, the end) value of 50,583 = 1,150.197726149283%. Also calculate the Actual Change (Absolute Difference, Variation) | Sep 23 16:40 UTC (GMT) |
| All the relative percentage changes calculated by users |
The relative percent change (the relative percent increase or decrease): 1. The absolute difference (the actual change). 2. The relative change. 3. The relative percent change. 4. Examples
1. 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 x value is the 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 (the actual change) between two values is not always a good way to compare two numbers.
- The actual change of one unit from the number 8 to the 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.
2. The relative change (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 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.
3. The relative percent change
- The relative percent change is the Relative change calculated as a percentage;
- The relative percent change = The relative change × 100/100 = (The relative change × 100)%.
4. Examples of calculating the relative percent change (increase or decrease)
- The relative change (from 2 to 3) = (3 - 2) / |2| = 1/2 = 0.5 = 50%
This change is a relative percent increase. - The 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%;
- The relative change (from 2 to -3) = (-3 - 2) / |2| = -5/2 = -2.5 = -250%
This change is a relative percent decrease. - The 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 percent decrease. - The relative change (from -2 to 3) = (3 - (-2)) / |-2| = (3 + 2) / 2 = 5/2 = 2.5 = 250%
This change is a relative percent increase. - The 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 percent increase.