Since,
1/3= .333(infinite) and
2/3= .666(infinite)
Why is it when you add 1/3 + 2/3 together, you get 1,
instead of .999(infinite) ( .333 + .666= .999)???
2006-07-29 14:50:58 · 36 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Proof of .99999999 (infinite) = 1 .....
Let x = .9 infinite
10x = 9.9 infinite
Subtraction of 10x-x
9x = 9
x=1.
2006-07-29 14:55:59 · answer #1 · answered by jlee1224 4 · 2⤊ 3⤋
1/2 +2/3 =3/3 3/3 is 1 .333 .666= .999 but the other is different
2006-07-29 14:53:15 · answer #2 · answered by Derrick G 2 · 0⤊ 0⤋
1/3 plus 2/3 = 3/3 = 1
.333 (infinite) plus .666 (infinite) = .999 (infinite) unless you round.
Once you get to calculus you will get the term limits
lim (x/9) (x->9) = 1 which basically means that .999 (infinite) eauls exactly 1.
2006-07-29 14:54:14 · answer #3 · answered by UOPHXstudent 4 · 0⤊ 0⤋
Fonzie,
.333(infinite) and .666(infinite) are inexact ways of expressing 1/3 and 2/3. The fractions are easily added whereas the decimal forms are not.
2006-07-29 14:58:42 · answer #4 · answered by benellis47 1 · 0⤊ 0⤋
When you add 1/3 and 2/3, you know exactly what you are dealing with. As for 0.333(infinite) and 0.666(infinite) - you do not the the full extent of these numbers and you can only use them as approximations. They are only approximations. 0.999... is DEFINITELY less than 1. Anyone who tells you otherwise is not very smart. This has nothing to do with analysis or calculus. It is based on the decimal number system. There is simply no proof that 0.999... is equal to 1.
2006-07-29 16:20:08 · answer #5 · answered by Anonymous · 0⤊ 0⤋
1/3 + 2/3 = 3/3 and therefore 1. Its just accepted that way. You can bet that if this was a question on a test you would get it wrong if you answered .9999. These types of numbers are almost always rounded up too.
2006-07-29 14:55:50 · answer #6 · answered by glitz2275 2 · 0⤊ 0⤋
Those who said that this is because 0.999 repeating EXACTLY equals 1 are correct. There is no rounding involved. No offense to those stating otherwise, but they are flat out mistaken on this matter. The question, "does 1= .9999....(repeating infinity)?" was asked by "Monkey" the other day: some of the folks had good answers, in case you want to look up this question.
Good observation-- excellent question, by the way.
2006-07-29 15:16:53 · answer #7 · answered by tom d 2 · 0⤊ 0⤋
The number is rounded off to 1
2006-07-29 14:53:07 · answer #8 · answered by Harry Cat 3 · 0⤊ 0⤋
actually there is no real fraction that has a decimal value of .999...
If it does then you just round it to one higher number higher.
For the fraction question, try adding in fractions. 1/3+2/3=3/3 or 1. Cause any number divded by itself is one, just in case you didnt know that.
2006-07-29 15:36:38 · answer #9 · answered by Anonymous · 0⤊ 0⤋
.999...etc.. is practically the same as 1. It rounds up. I know it's confusing, but think about it. when u buy something in the store and it's $1.99..how much do u really say it is? $2. you round up the .99. hopefully that comparison helped u to understand it.
2006-07-29 14:54:57 · answer #10 · answered by C O 2 · 0⤊ 0⤋
if you study the limits of infinite series in calculus, there are proofs/questions/exercises that will show you.... its the type of stuff no one except a math professor remembers... and hell.... no one really uses it.
so (0.3333....)can be written as an infinite series, and (0.6666).... take the limits of both of these functions, you get 1/3 and 2/3.....add and u get 1
just ask a college math prof or read a calculus book
2006-07-29 14:55:41 · answer #11 · answered by drfghdfghdfgh 2 · 0⤊ 0⤋