Shouldn't Math be Perfect?

Question

My husband and I were discussing mathematics the other day (it was a long drive home ^_^), and we came across some interesting things that I hadn't thought of before. And I think most people probably haven't, either. We just accept it.
It turns out that math really is imperfect. The phrase is "numbers don't lie" but I think they do!!
Here is one problem that we couldn't find an answer to:
*Why is it that* when you divide 3 into 100 you get 33.3 repeating, but when you *multiply* 3 by 33.3 reapeating, you get... 99.9 repeating! It should get you back to 100, but it doesn't. Shouldn't it work both ways?? Like, when you divide 3 into 12 you get 4, and when you multply 3 by 4 you get 12. It works. Numbers should always work, but they often don't! Why!??
^__^ Sorry for the rant, but it's really interesting... when you think about it. :)

Answer 1

Math is perfect :)

In the example you gave above, 99.9 repeating, is, believe it or not, THE SAME NUMBER as 100!

Yep, this comes from the fact that 0.999 repeating equals 1.

Short proof : 1/9 = 0.111 repeating
(1/9) * 9 = (0.111...) * 9
1 = 0.9999...

Answer 2

Math is only imperfect to the imperfect people that created it. The most basic example would be infinites versus human logic. Total contradiction. Like time... when did time start and when will it stop? our technology and research shows that EVERYTHING must start and stop in real life. does light truly travel at 186,000 kilometers per second or is there a hidden friction that we are not seeing that is slowing it down? Our mind is predetermined to always ask the question "why" and imagining 33.333 to the end of the universe and beyond is too much for us to comprehend.. speaking of that, how far away is the end of the universe.. i think you get my point by now... if not, i can prove to you that 2+2=5

2+2=5
whatever you do to one side of the equation, do to the other..

2A+2A=5A
combine matches

4A=5A
set A to equal 0

4(0)=5(0)

0=0

2+2=5

just our imperfect minds....

Answer 3

IT didn't turn back into 100 because you were using a calculator that forces answers to be rounded off. Suppose your calculator only holds 8 digits, and you enetred 100 / 3. You would get 33.333333. To the calculator, there are noi more threes. So when you multiply this by 3, you get (exactly) 99.999999.

The flaw is not with the math, it's with the machine.


Don't get me wrong, math is still not "perfect." A better phrase would be "well-structured."

Answer 4

It is perfect.
Techically 100 divided by 3 is 33 and one third. The Three repeating is just the closest decimal equivalent, not the exact answer.

Answer 5

My smart *** comment is: "That's why in math there are such things as imperfect numbers-math would be perfect if it weren't for the imperfect numbers." But seriously, my contention is that any signifier which takes the place of nature, assuming nature is really 'perfect', fails perfection because it is only a representation of truth. Words can construct ideas, as can numbers, and so we can only expect to find them as perfect as they are applied. It is typical of naive human intelligence to assume that our own inventions are divine in there own right . . . we forget that they didn't just drop from heaven! Math is not perfect, and even though its proofs give the sensation of being 'set in stone', it takes a lot of creativity, rule breaking, and luck to get to those great new breakthroughs!

Answer 6

it does work, because whenever there is a .9 repeating, it is rounded up to the nearest 1, so 99.9 repeating, is actually 100, its a stupid rule but thats the reason its in place

Answer 7

Open a book - those repeating decimals repeat infinitely.... they don't just stop and give an incorrect answer!

Answer 8

Math easy

Answer 9

99.999... is actually equal to 100.
(10)(99.999...)=999.999...
let x=99.999...

10x=999.999...
subtract x=99.999...
then 10-x=999.999...-99.999...
9x=900
x=100

Answer 10

math sucks!