No mattter how far down the line you go with .999~, you'll still be short that .1 somewhere. I'm tired of people saying that .999~=1 when it doesn't.
2006-12-31 12:41:58 · 25 answers · asked by Derek B 1 in Science & Mathematics ➔ Mathematics
S = 0.99999999999 ...... infinity (1)
Multiplying both sides by 10
10 S = 9.999999999 ........ infinity (2)
Subtracting (1) from (2)
9S = 9
So S = 1
2006-12-31 12:45:41 · answer #1 · answered by Sheen 4 · 3⤊ 0⤋
It does if the line of 9's is infinite, because for them to not be equal there must exist a definite gap between the 2 numbers with a value greater then zero. That .1 difference happens after an infinite amount of 9's, so it never happens.
So the question is this, What is 1 minus .999~ with an infinite amount of 9's? The answer is 0 because you'll never find the .1 that happens after the infinite number of 9's.
This 1 - .999~ = 0 and 1 = .999~
2006-12-31 20:46:36 · answer #2 · answered by moronreaper 2 · 3⤊ 0⤋
no rounding up needed
1/9 = 0.111111111111...
2/9 = 0.222222222222...
3/9 = 1/3 = 0.3333333333333...
4/9 = 0.444444444444...
5/9 = 0.555555555555...
6/9 = 2/3 = 0.6666666666666...
7/9 = 0.777777777777...
8/9 = 0.888888888888...
9/9 = 0.999999999999...
but 9/9 = 1
The problem people are having is that 0.99999... goes on forever. The answers that pointed out that there is no difference between 1 and 0.999999... are right. Try this: write down 1.00000000... - 0.99999999... Put the 1 over the 0.999... Now do what you would need to do to subtract. 0 - 9 means you need to "borrow" from the previous digit. This means the 1.000... becomes 0.999999...
There is no end to this so 1.00000... - 0.9999999... = 0
2006-12-31 21:02:06 · answer #3 · answered by smartprimate 3 · 2⤊ 0⤋
here is a somewhat mathematical proof, at an Algebra 2 level:
The formula for the sum of a convergent geometric series is this, proven in Pre-calc and Math 252:
A1/(1 - r) where A1 is the first term, and r is the ratio of each term to another.
r has to be < 1, by defintion of convergence.
Let A1 be .9
let r be .1: .9 x .1 = .09
This will mean:
.09 + .9 = .99
.09 x .1 = .009
.009 + .09 + .9 = 1
the process keeps repeating to get .999999.........
So plug the stuff back into da formula:
A1/(1 - r) = .9/(1 - .1) = .9/.9 = 1
there.
2006-12-31 21:40:30 · answer #4 · answered by MT5678 2 · 2⤊ 0⤋
This is by far one of the most controversial topics in math, because it gets bombarded by those who don't grasp the concept of infinity enough to realize it, in addition to the hardcore mathematicians who KNOW this is true.
The fact of the matter is that it's NOT short that 0.000000~1 somewhere, because if there was a 0.00000~1 somewhere, that would suggest 0.0000~1 stops. But it DOESN'T. You can't have an infinite number of 0 ending in a 1, because ENDING would indicate it's not infinite!
Have you covered infinite series yet? It's a grade 12 topic. It proves that the infinite series 9/10 + 9/100 + 9/1000 + ..... is equal to 1. It's a concept people refuse to grasp because it seems to be short that little bit when there's no little bit at all to be short of.
If two numbers are unique, then there exists a number in between them. There does NOT exist a number in between
0.999~ and 1.
2006-12-31 20:46:18 · answer #5 · answered by Puggy 7 · 4⤊ 2⤋
so .999 = 0 ? or closer to 1 ?
2006-12-31 20:45:15 · answer #6 · answered by cork 7 · 1⤊ 0⤋
ok, now let see,
if you have ever study limit, you will know
lim 10^-x when x run to infinite is 0
however, 10^-x equal 0.000000000000...00001 ( x - 1 number 0)
and if you add 0.99999999999999...99 ( x number 9 ) to it it become 1 ( eg 0.1 + 0.9 = 1)
and we know from above that limit of 10^-x = 0
so we can say that 0.99..999 equals to 1
2006-12-31 20:51:02 · answer #7 · answered by giovabao 2 · 1⤊ 0⤋
.999=1 if it is rounded off
2007-01-01 08:37:19 · answer #8 · answered by Nitin T F1 fan 5 · 0⤊ 1⤋
This is rounding. When you round 0.999 it rounds up to 1.0 or 1. Rounding is used more than you think. It is easier to remember, use, and pictures numbers in this fashion. When you purchase something and it is priced at $14.99. It is very close to $15.00. After taxes it is going to be $15 and something cents anyway. This is an easy amount to figure. Say if I was going to purchase something cost $1487.99 and I had a limit. It would be much easier to figure out the tax at $1500.00 without a calculator. The tax would be about $125.00.
2006-12-31 20:59:47 · answer #9 · answered by Anonymous · 0⤊ 2⤋
wrong. you'll be short that .001 then .0001 then .00001 eventually .000000000000000000000000001, which is so close to a 0 difference b/w the numbers that .999 is about 1
2006-12-31 20:43:56 · answer #10 · answered by Anonymous · 1⤊ 2⤋