33.33(33.33%)+33.33(33.33%)=66.66 (66%) How is (33.33+33.33+33.33=100)? And not 99.99 No matter how many 3´s you add behind the decimal it´s still gonna be 9´s stacked?
+23251 33 1/3 % is 33.33333333... [with the threes never stopping]
and 33 1/3 isn't exactly 33.33 [33.33 is only an approximation]
So: 33 1/3 + 33 1/3 + 33 1/3 is 100 [exactly].
And: 33 1/3 + 33 1/3 + 33 1/3 = 33.333... + 33.333... + 33.333...
= 99.999... [with the nines never stopping]
So, why does 99.999... equal 100?
Two different arguments (both correct);
First. If you have two different numbers, there must be another number between them (actually many numbers between them). So, if 99.999... and 100 are different number, what is a number between 99.999... [remember that the nines never stop]? No one can find another number between them, so they must be the same number.
Second: an algebra proof.
Call the number n to equal 99.999... and also find 100n which is 9999.999... and subtract them:
100n = 9999.999999999999999...
n = 99.999999999999999...
Subtracting: 99n = 9900.000000000000000...
Dividing by 99: n = 100.0000000000000000... or, more simply, 100
Therefore, 99.999... = 100
