Hat Trick Maker Posted July 21, 2012 Share Posted July 21, 2012 Guys, I'm no math whiz, but I think the issue depends on whether you assume a repeating decimal as an approximated representation or as an equal representation of the fraction in question. The convention is that we take it as an equivalent of the fraction. For instance, 1/3 = 3/10 + 3/100 + 3/1000 + 3/10000 + ... = .3 + .03 + .003 + .0003 + ... = .3333... To understand why the series 3/10 + 3/100 + 3/1000 + 3/10000 + ... is equal to 1/3, just visualize how long division will work on 1/3. That is, 1 ÷ 3 = .3 (i.e 3/10) with a remainder of .1 which will be divided by 3 to yield .03 (i.e 3/100) with another remainder of .01 which will again be divided by 3 and so on. If we imagine that the series 3/10 + 3/100 + 3/1000 + ... will go on forever (cue Titanic theme song), it will eventually be equal to exactly 1/3 and this is not an approximation. It is in this sense that we say .9999... is equal to 1. As babych pointed out, some of us have a hard time convincing ourselves because their thought process truncates the number and assumes it as a finite number which will of course be only an approximation. Personally, I think this practice is made out of convenience. For example, a calculator will only remember the answer to 1 ÷ 9 as 1/9 even though the output is shown as .1111... for it cannot genuinely store an infinite number in the memory. That explains why you get an answer of 1, rather than .9999... when you add the output of 1 ÷ 9 to 8/9: 1 ÷ 9 = .111111111 ANS + 8/9 = 1 Whether you recognize a repeating decimal as an approximation or as an exact equal is arbitrary. It is not like there is some indisputable evidence in the factual world that proves .9999... is 1. This is a matter of convention. EDIT: Silly mistakes corrected. Link to comment Share on other sites More sharing options...
GodzillaDeuce Posted July 21, 2012 Share Posted July 21, 2012 This just goes back to the limitations of decimals that I've been talking about this entire time. If you fail to accept decimals as an imperfect way of describing fractions, then you will always reach your conclusion of them being equivalent. However, if you see the problem with a decimal representing something that goes on for infinity, then my conclusion is the logical one. This is my conclusion from this debate that has gone on for too long. 2 conclusions can be reached, it just depends on how one views decimals that decides which one is chosen. Link to comment Share on other sites More sharing options...
babych Posted July 25, 2012 Share Posted July 25, 2012 Guys, I'm no math whiz, but I think the issue depends on whether you assume a repeating decimal as an approximated representation or as an equal representation of the fraction in question. The convention is that we take it as an equivalent of the fraction. For instance, 1/3 = 3/10 + 3/100 + 3/1000 + 3/10000 + ... = .3 + .03 + .003 + .0003 + ... = .3333... To understand why the series 3/10 + 3/100 + 3/1000 + 3/10000 + ... is equal to 1/3, just visualize how long division will work on 1/3. That is, 1 ÷ 3 = .3 (i.e 3/10) with a remainder of .1 which will be divided by 3 to yield .03 (i.e 3/100) with another remainder of .01 which will again be divided by 3 and so on. If we imagine that the series 3/10 + 3/100 + 3/1000 + ... will go on forever (cue Titanic theme song), it will eventually be equal to exactly 1/3 and this is not an approximation. It is in this sense that we say .9999... is equal to 1. As babych pointed out, some of us have a hard time convincing ourselves because their thought process truncates the number and assumes it as a finite number which will of course be only an approximation. Personally, I think this practice is made out of convenience. For example, a calculator will only remember the answer to 1 ÷ 9 as 1/9 even though the output is shown as .1111... for it cannot genuinely store an infinite number in the memory. That explains why you get an answer of 1, rather than .9999... when you add the output of 1 ÷ 9 to 8/9: 1 ÷ 9 = .111111111 ANS + 8/9 = 1 Whether you recognize a repeating decimal as an approximation or as an exact equal is arbitrary. It is not like there is some indisputable evidence in the factual world that proves .9999... is 1. This is a matter of convention. EDIT: Silly mistakes corrected. Link to comment Share on other sites More sharing options...
JohnLocke Posted July 25, 2012 Share Posted July 25, 2012 I want to play. What number comes up if 1 is divided by infinity? Link to comment Share on other sites More sharing options...
D-Money Posted July 25, 2012 Share Posted July 25, 2012 OP - what are you rounding to? Whatever it is, the last digit of should be a 7... 0.667 0.666666666667 0.66666666666666666666666666666666666666666666666666666666666666666666666667 Hence, add that to 0.333... (same number of digits), and you get 1 - not 0.999... Didn't anyone teach you how to round numbers? Link to comment Share on other sites More sharing options...
babych Posted July 25, 2012 Share Posted July 25, 2012 OP - what are you rounding to? Whatever it is, the last digit of should be a 7... 0.667 0.666666666667 0.66666666666666666666666666666666666666666666666666666666666666666666666667 Hence, add that to 0.333... (same number of digits), and you get 1 - not 0.999... Didn't anyone teach you how to round numbers? Link to comment Share on other sites More sharing options...
sulihpoeht Posted July 25, 2012 Share Posted July 25, 2012 I give up. Link to comment Share on other sites More sharing options...
JohnLocke Posted July 25, 2012 Share Posted July 25, 2012 Just wikipedia 0.999.. It gives a really good explanation of why it = 1 and also explains why people (like some people in this thread) don't want to accept it. Link to comment Share on other sites More sharing options...
Argon Posted July 26, 2012 Share Posted July 26, 2012 oh common guys. it's impossible to have exactly 1/3 of something, you can only round or astrisk an infinity of numbers. so therefore it should be impossible to assume that 3 thirds can equal something so definitive as 1 =/= 1 theoretically speaking it's an interesting idea, but mathimatically it's the equivelant of playing video games. Link to comment Share on other sites More sharing options...
babych Posted July 26, 2012 Share Posted July 26, 2012 oh common guys. it's impossible to have exactly 1/3 of something, you can only round or astrisk an infinity of numbers. so therefore it should be impossible to assume that 3 thirds can equal something so definitive as 1 =/= 1 theoretically speaking it's an interesting idea, but mathimatically it's the equivelant of playing video games. Link to comment Share on other sites More sharing options...
Gurn Posted July 26, 2012 Share Posted July 26, 2012 Just say you shoot an arrow at a target. When it travels to its target, it has to go half way, then half of rest of the way, then half of the rest of the way, then half of the rest of the way... and so on, forever. This formula shows that the arrow will never be able to get to the target, which is why 1=0.9999... Link to comment Share on other sites More sharing options...
mpt Posted July 26, 2012 Share Posted July 26, 2012 What a retarded question... Gotta love the future of our youth... Link to comment Share on other sites More sharing options...
.Naslund Posted July 27, 2012 Share Posted July 27, 2012 1/1 = 0 not srs Link to comment Share on other sites More sharing options...
undahbile Posted July 27, 2012 Share Posted July 27, 2012 0.999... = 1 for the same reason 1.000... = 1. Link to comment Share on other sites More sharing options...
Columbo Posted July 27, 2012 Share Posted July 27, 2012 That was a really dumb question. Here is an actually simple question that is more complicated than it looks: 6÷2(1+2) = ? Link to comment Share on other sites More sharing options...
-Vintage Canuck- Posted July 28, 2012 Share Posted July 28, 2012 That was a really dumb question. Here is an actually simple question that is more complicated than it looks: 6÷2(1+2) = ? Link to comment Share on other sites More sharing options...
trek Posted July 28, 2012 Share Posted July 28, 2012 The poll results of this question cause me great concern... Link to comment Share on other sites More sharing options...
greenbean30 Posted July 28, 2012 Share Posted July 28, 2012 The poll results of this question cause me great concern... Link to comment Share on other sites More sharing options...
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