if 1/3=.333333......
and 2/3=.66666666666666666666
does that mean .99999999999........=3/3
2006-11-06 14:41:33 · 9 answers · asked by lookadistraction 4 in Science & Mathematics ➔ Mathematics
Yes, it does. 0.999999999999999 repeating = 1.00000000000
2006-11-06 14:43:56 · answer #1 · answered by urbancoyote 7 · 0⤊ 0⤋
It's true that .9999999.... = 3/3 = 1 = 1.000000....
This can work because for some real numbers there is more than one decimal expansion.
If we look at the meaning of this,
1.000000.... = 1 + 0*(1/10) + 0*(1/100) + 0*(1/1000) + ...
and
0.999999.... = 0 + 9*(1/10) + 9*(1/100) + 9*(1/1000) + ...
These two sums add up to the same number: 1. This comes from that if we accept infinite decimal expansions then we must accept infinite sums (Note: if we don't accept infinite decimal expansions then we'll have problems with division, i.e. what would be the expansion of 1/3?). So by this acceptance, it turns out that some numbers (namely the ones we can represent as a terminating decimal) have two representations.
Example:
.236 = .2360000000... = .2359999999...
since .000999999... = .0010000...
If you want to learn more, you can ask someone about geometric series or decimal expansions of real numbers. This link contains a good explanation of .999... = 1. Cheers!
2006-11-06 23:26:12 · answer #2 · answered by bag o' hot air 2 · 0⤊ 0⤋
Nope.
However many 3's you have for 1/3, you need one less 6 and the string of 6's ends with 7 for the equivalent 2/3.
e.g.
.33333333
.66666667
At SOME point, you have to round up.
2006-11-06 22:46:13 · answer #3 · answered by WindWalker10 5 · 0⤊ 1⤋
I just recovered from a hallucinagenic drug trip, so I really DON'T need to think about this much longer than 1-second.... sorry Dude.
.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 is 3/3 or 1..... except for that last .00000000000000000000000000001000000000010000000000000000000000000000000001
Now if I was high, this MIGHT be some freaky sh*t you're laying down and might keep my mind busy for, oh, I dunno....2-seconds?
I take it you're not a Math major?
Policeman: "Put your hands in the air and step away from the weed!"
2006-11-06 22:54:31 · answer #4 · answered by Chong Connery 2 · 0⤊ 1⤋
Yes. The impllication is that all the decimal expansions are carried infinitely. If that is not so, then there will be a tiny difference between .99999... and 1.
2006-11-06 22:44:06 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Well, .999999.... still does not equal to 1 so it can't be 3/3
2006-11-06 22:45:59 · answer #6 · answered by Cecilia 2 · 0⤊ 1⤋
I´m thinking!
3/3 = 1
2,99999999.../3 = 0.999999...
2006-11-06 23:02:32 · answer #7 · answered by Colorado 4 · 0⤊ 0⤋
I'm not so good at this stuff but yes !
2006-11-06 22:50:23 · answer #8 · answered by Anonymous · 0⤊ 0⤋
yeah, sound good !!!
2006-11-06 22:44:29 · answer #9 · answered by ? 3 · 0⤊ 0⤋