are these two things the same?
2007-09-04 12:13:56 · 12 answers · asked by computer whiz 5 in Science & Mathematics ➔ Mathematics
Yes. Think of it this way...
1/3 = 0.3333333.... right?
So what does (3)(1/3) equal? You would say 1, right?
And (3)(0.3333333....) = (0.999999999....)
So (0.99999999999....) = (1).
Okay, it's not a proof worthy of the greats, but I think it ties it up nicely.
2007-09-04 12:18:23 · answer #1 · answered by Lucas C 7 · 5⤊ 0⤋
If the 9 recur infinitely, yes.
1 = 9/9 = 9 x 1/9 = 9 x 0.1111111(recurring) = 0.999999(recurring)
2007-09-04 12:23:51 · answer #2 · answered by Beardo 7 · 3⤊ 0⤋
Yes they are equal here is why.
.999999999999(Repaeatin)=X
Multply both sides by 10
9.99999999999(Repeating)=10X
minus .999999(repating) from both sides rememberrr x=.9(repeating)
that means 9=9x
meaning that X=1
and since X=.99999999(Repeating)
.999999999(Repeating)=1
2007-09-04 12:18:57 · answer #3 · answered by Mr. Smith 5 · 0⤊ 0⤋
Another way to look at it is, if 1 and 0.999999.... repeating are different numbers, then there has to be a number in between them. I can't find a number between them.
2007-09-04 12:22:26 · answer #4 · answered by thomasoa 5 · 3⤊ 0⤋
this is a topic for advance calculus.
but the assumption goes as this: the limit of .999 as it goes to infinite is assumed to be 1.
it's called convergences. google it, or use the wikepidia to explain series and limits
2007-09-04 12:17:58 · answer #5 · answered by nathan 6 · 0⤊ 1⤋
This question has been asked so many times, that puggy (top contributor) has actually posted the answer to this question in his profile.
http://answers.yahoo.com/my/profile;_ylt=AtcX01cWCxYnKVLtHFy.4iH.0KIX?show=8b24df9325c99ab13f9f6d0244219134aa
2007-09-04 12:23:08 · answer #6 · answered by Dr D 7 · 4⤊ 0⤋
Yes, u can say that. The difference is infinitely small.
2007-09-04 12:17:04 · answer #7 · answered by Legend 3 · 0⤊ 2⤋
no they r different .99999999999 will always be .00000000001 smaller than 1
2007-09-04 12:18:29 · answer #8 · answered by no name 1 · 0⤊ 6⤋
yes.
If x=0.999...
10x=9.999...
then,
10x - x = 9.999... - 0.999...
which simplifies to
9x = 9
and
x=1
2007-09-04 12:18:38 · answer #9 · answered by Loyal2UIL 2 · 4⤊ 0⤋
Yes.
They are equal.
2007-09-04 12:17:20 · answer #10 · answered by Vincent G 7 · 3⤊ 1⤋