Well I was wondering in my math class today how 3/3 equals 1? The reason I am asking this is because doesn't 1/3 = .3333333.....? So 2/3 would = .666666... Right?

Well then my question is, wouldnt 3/3 = .99999999999 and not equal 1?

I know this must sound like a n00b question but I just want to know the logic invloved that makes 3/3 = 1. I understand that we round it up but why? Please and thanks to all that can help me.

Troll?

There is no rounding involved. .999...( with the 9's repeating indefinitely) is exactly equal to 1. Thus 3/3=.999...=1. There are many proofs of this online and in the totse archives.

Haven't seen one of these in a while, thank god.
But now the argument rears its ugly head on a Monday night.

*goes hangs himself*

You have it backwards...

(1/3) * 3 = 1.

1/3 = 0.3_ (even those this is INCORRECT because you cannot EVER TRULY have 1/3 in a decimal form because even AFTER an infinite amount of threes you'd still never have that one-third of a number you need to make it truly one third. It's an error with the way our mathematics was designed.)

Makes sense?

It all actually has to do with calculus and infinite series of numbers.

.9999999999... = .9 +.09+.009+.0009+.00009+....

.9 = .9*10^-0
.09 = .9*10^-1
.009 = .9*10^-2
...etc...
.9*10^-inf

so when we write it using a sigma (I'll try):
.9* [sigma from n=0 to infinity] 10^-n

10^-n is the same as (1/10^n) which is (1/10)^n
so now it's a geometric series.... this is where calculus is used
where a=.9 and r=1/10

.9/(1-1/10)=1

It makes about as much sense as two missiles turning into a whale and a pot of flowers, but it's a mathematical reality...

It's the same kind of thing which proves that e^(i[pi])=-1 freaky stuff, isn't it?

the real, most accurate, proof online:
http://en.wikipedia.org/wiki/Infinite_series_of_nines

also, if this weren't true: http://en.wikipedia.org/wiki/Zeno%27s_paradoxes

Infinity cannot be used within our system of math.. It's something that we BARELY understand, so trying to deal with it in math. will only end with us making idiotic mistakes like this.

we dealt with it all the time in calculus and didn't seem to have any problems...

It's understood in mathematics, just not very well conceptually by a lot of people.

Three-thirds is 1. But since 3/3 is not .99, because .33 is an approximation.