This is less of a question, and more of a surprising statement, but does anyone agree with this? Here is the problem in question:
x = 0.9999...
10x = 9.9999...
10x-x = 9
9x = 9
x = 1
(Sorry about the '=' signs not lining up, the software has done this)
Now look at how the first and last answer vary. If I started with 'x' equalling 0.9999 recurring, how does the last answer mean 'x' equals 1?
Any answers?
P.S. Please stay away if you do not have a real answer (genuine statements only please)
2007-07-03 07:23:13 · 12 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Thank you for the comments so far. Some of which are perfectly correct, some, however, are not.
Those of you that think 10x-x = 8.9991, are wrong. You have simply type the sum (9.9999 - 0.9999) into a caluculator, and it has given you that answer.
If you look closely at what the calculator is doing, it changes the 9.9999 into a 9.99. So this this menas that 9.99 - 0.9999 is obviously not the correct way of doing it. (I am refering to the Microsoft PCs calculator, which does it this way, many other calculators do it this way too)
Thanks again for the answers with a bit of thought in them, that was what I was after.
2007-07-04 05:01:56 · update #1
You, and the first answerer DavidK93, are both correct. Every two or three weeks, there is a question about this, and a huge range of answers, mostly wrong ones.
2/3 and 4/6 are two different ways of writing down exactly the same number.
1, and 0.9999... infinitely recurring, are two different ways of writing down exactly the same number, and there's no point in arguing about it. However, one of these ways involves an infinite series, so an apparently correct argument can come to the wrong conclusion. This is what happens in Zeno's paradox about the race between Achilles and the tortoise.
2007-07-03 10:16:27 · answer #1 · answered by Anonymous · 1⤊ 0⤋
The suggestion here is that we are working with recurring numbers. The reality is...that we are not.
If x = 0.9999 then 10x = 9.999 (not 9.9999)
So 10x - x is 9.999 - 0.9999 = 8.9991
So 9x = 8.9991
Divide both sides by 9
x = 0.9999
2007-07-03 08:29:55 · answer #2 · answered by brainyandy 6 · 0⤊ 1⤋
9x does not equal 9 for a start. So how can 'x' be anything other than 0.9999 recurring.
2007-07-03 07:41:08 · answer #3 · answered by Anonymous · 1⤊ 1⤋
I've seen this example before, the two ways it was explained to me at the time makes sense.
1. .999 repeating, truly does equal 1. Why? well can you tell me how much less than one it is? what is 1-.99999999 repeating? How far back does it repeat? well forever, so 1-.9999... is 0! hence 1=.9999999.....
2. Think of 1/3+1/3 +1/3 as we know this should equal one, well, what if we change these to decimals first. then add, we SHOULD get the same answer, but,
.3333 repeating, + .3333 repeating +.3333 repeating =.9999repeating, again.999999......=1
2007-07-03 07:32:30 · answer #4 · answered by Have_ass 3 · 2⤊ 0⤋
suppose this number is 0.9999 and not 0.9999....
Then, 10 * 0.9999 = 9.999
Thus, 9.999 - 0.9999 = 8.9991
Therefore, when you say that 10x - x = 9 you are approximating the value 8.9999.........9991 to 9
Hence, 9x is actually equal to 8.9999999999.....991
bringing the value of x to its original value of 0.9999999...
2007-07-03 07:45:13 · answer #5 · answered by amol d 1 · 0⤊ 1⤋
No!....No!.....No!.....
10x -x = (10 - 1)x = 9x = 9 * 0.9999 = 8.9991
2007-07-03 09:04:11 · answer #6 · answered by Anonymous · 0⤊ 1⤋
Now i cant say i'm sure if it is true. The thing is my math teacher is literally a pioneer in mathematics and he says that it is only true if 4 the equation, you can work backwards. So from 1 equals x, can u use the same logic to get to x equals 0.999999999... If not then the statement cannot be true
2007-07-03 07:34:21 · answer #7 · answered by dirtbagsimon 1 · 0⤊ 1⤋
This is interesting. I guess nobody said infinity is perfect...
Mathematicians agree that it equals 1, huh? I might be tempted to think that 0.999 is irrational, since there is no p/q that equals it. Since it is irrational and 1 is not, they cannot be equal - they are not even in the same domain of numbers. Therefore I would conclude that 0.999... approaches 1 but never equals it.
2007-07-03 07:48:40 · answer #8 · answered by Gary H 6 · 0⤊ 1⤋
This is an infinite series:
x = .9 + .09 + .009 + .0009 + ...
It goes on forever.
It can get as close to 1 as you like.
Mathematicians agree that it is 1.
There is something unsatisfying about this. But if it's not 1, what number would you say it is?
2007-07-03 07:28:48 · answer #9 · answered by fcas80 7 · 1⤊ 0⤋
Your work successfully proves that 0.999 recurring is equal to 1.
2007-07-03 07:28:14 · answer #10 · answered by DavidK93 7 · 2⤊ 0⤋