|
I guess it's school related, it's a mathematical wonderment
Does .9 infinitely repeating equal 1? At first glance, one might say, "Of course not!", but hear me out. I asked my genius math teacher the same question, and he though about it, then wrote a long equation apparently proving that they were the same number. I have since then forgotten the equation, therefore, forgotten how he arrived at his conclusion. A fellow classmate said he would argue to the death that they were not, but his opinion changed upon reading the teacher's equation. My way of thinking it is this: If 3 x 1/3=1, and 1/3= .3 infinitely repeating, then .3 infinitely repeating should equal 1. But if do the multiplication, each individual 3 would become a 9, so the answer is also .9 infinitely repeating. So 1/3 x 3= 1= .3 infinitely repeating x 3= .9 infinitely repeating. So 1= .9 infinitely repeating. But to say that two different numbers, excluding fractions, etc, can equal the samething doesn't seem right. So, are they or are they not equal?
[ ]
Want to answer more questions in the Work & School category?
Maybe give some free advice about: School?
Yes, if you have .99999 infinitely repeating, it is equal to 1. (In fractions you could say that it's 9/9. 1/9 = .11111 infinitely repeating, 3/9 or 1/3 = .33333 infinitely repeating, and so on.)
That's the thing about infinity: it does wacky things to numbers ^_^
]
hmm . . . don't think they're equal, but I'm not a math teacher. In class my math teacher was talking about the infinite number of numbers between any two numbers thing (O_O) and she told us about the guy who came up with that.
His friend thought he was stupid, so told the friend to walk halfway across a room. Then halfway across the remaining half. And halfway across that. And so one and so forth.
Stick your .9999999 infinite repeating question in there, and I don't think they're the same at all.
]
welcome to the world of rounding... that is where the error is that you fail to compensate for. 0.333333333 X 3 = 1, not 0.9999999(ad nauseum).
Rounding.
I read your reply... you are forgetting that 0.33333(infinity) is not the same as 0.3333 (4 decimal places). 0.3333 x 3 is indeed 0.9999
but 0.333333(infinity) x 3 = 1
the decimal version of 1/3 is an infinite fraction... the visual of that, being 0.3333(infinity) is an approximation.
The answer, wether you like it or not, is rounding. 0.3333 + 0.6667 = 1 is it not? why do I show 2/3 as 0.6667? Because of ROUNDING.
0.999999(infinity) is not 3/3, instead it is "very close to one", and yes, 0.9999(infinity) rounds up to 1. Does that make them equivalent? No.
When you have 0.3333(infinity), you have to remember that those 3's keep going forever. Infinity is a rather tricky concept. Remember that 0.3333(infinity) is 1/3, thus 0.6666(infinity) is 2/3... but as I said, 0.6666(infinity) rounds up to 0.6667 so clearly, 3/3 is not 0.9999(infinity) but is indeed just the number One.
]
More Questions: |