Heavenly Half-Percentages

Dividing a number by 2 gives you the number's half. This is also the reason why ½ is the reciprocal of 2. The word percent in mathematics means to divide the number by 100; "X% of Y" means "Divide X by 100, then multiply by Y". Half of a percent is what you get when you divide X by 200 (Since 100 × 2 = 200 & 1/100 × ½ = 1/200) then multiply by Y. So, if you check out the function below...

(X/2)% of X = X²/200

Here's a T-table of integers from 0 to 25 in which the function above is used(percentage of X included in 3rd column):

X	Y	% of X
0	0	0%
1	0.005	0.5%
2	0.02	1%
3	0.045	1.5%
4	0.08	2%
5	0.125	2.5%
6	0.18	3%
7	0.245	3.5%
8	0.32	4%
9	0.405	4.5%
10	0.5	5%
11	0.605	5.5%
12	0.72	6%
13	0.845	6.5%
14	0.98	7%
15	1.125	7.5%
16	1.28	8%
17	1.445	8.5%
18	1.62	9%
19	1.805	9.5%
20	2	10%
21	2.205	10.5%
22	2.42	11%
23	2.645	11.5%
24	2.88	12%
25	3.125	12.5%

If you exclude the percent sign(%) in the 3rd column, every number in that column is half of the number in the 1st column! (It's true for each row!) I put the half-integers & other non-integers in the 2nd column in decimal form for quickness & ease. All odd numbers have half-integers as halves; even numbers have whole integers as halves!

Any percent of zero is still zero because you would have to multiply by zero! (You know what the product will be!)

X can be any real number you want in this eXcellent function! Get it? I capitalized the "X" in excellent! The dependent variable Y will never be undefined! Dividing the square of X by 200 will give you the number in the 2nd column for each row!

Here's an interesting example: If X = the square root of 2, then Y = 0.01 in this function! That non-integer is rational! Half of the square root of 2 is also its reciprocal, by the way!

To find a number's reciprocal, raise it to the power of -1; it's an exponential property.

Note: This function also works with imaginary numbers, but the dependent variable will be negative. With complex numbers, (a real number + an imaginary number) the dependent variable will be an imaginary number.

By the way, x% of x is x squared divided by 100.

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© Derek Cumberbatch