2006-10-12 16:08:41 · 6 answers · asked by alphabetagamma34 2 in Science & Mathematics ➔ Mathematics
Yup had the answer mostly correct. And no laws are violated. The answer is simply that there's no reason a decimal can't go on forever. In the case of .9 repeating, it equals 1. Yup's proof was pretty much on the money, but I think the formatting makes it a bit confusing. So I'll try to explain.
Let's suppose that x = .999....
Then 10x = 9.999.... (since multiplying by ten just moves the decimal point)
If we subtract x from 10x, we obviously get 9x.
9.999... - .999 = 9
So now we have 9x = 9. Dividing by 9 gives us x = 1.
Another way to look at it is that any single-digit number over 9 equals a repeating decimal. For example:
1/9 = .111...
2/9 = .222...
9/9 = .999...
2006-10-12 16:25:09 · answer #1 · answered by howdowncat313 1 · 0⤊ 0⤋
Basically, .9999999999...=1.
There is actually a lot of mathematical work that has gone into proving this to be true. There's a looooong discussion of the matter on Wikepedia, with plenty of references.
2006-10-12 16:36:12 · answer #2 · answered by just♪wondering 7 · 0⤊ 0⤋
the only way is to follow this concept
(1/3) + (2/3) = .33333333333 + .66666666666 = .999999999999
the only thing is, the actual value is
.333333333 + .6666666667 = 1
2006-10-12 16:37:57 · answer #3 · answered by Sherman81 6 · 0⤊ 0⤋
1 - .00000000000000000000000000000001
2006-10-12 16:18:53 · answer #4 · answered by mystic_golfer 3 · 0⤊ 1⤋
0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 ok but i think .9... is 1 cause
x=.9...
*10 *10
10x=9.9...
-x -x
9x=9
/9 /9
x=1
soo idk really
check that cause i'm pretty sure it goes against some laws.
2006-10-12 16:17:10 · answer #5 · answered by Yup 2 · 0⤊ 0⤋
lets see : 9/1 \ 011
...................10
......................9
....................-----
.......................10
.........................9
.......................-----
.........................10 etc etc etc
YES if I multiply this with 9 I get 0.999999999999999
2006-10-13 01:49:18 · answer #6 · answered by gjmb1960 7 · 0⤊ 0⤋