0.999... The Truth! Quiz

What do I do?	Do the math!
We'll start off with 0.333... (there are infinite threes after the point) Understand?
Now, tell me what FRACTION 0.333... is (when cancelled down)
Okay, so multiply 0.333... by 3 now.
Now, multiply your fraction (second answer) by 3. (Keep the same denominator!)
So, those last two answers... are they EQUAL, or UNEQUAL? (Hint: they start off the same, and you multiply them by the same amount)
But wait, that fourth answer there... what WHOLE NUMBER is that equivalent to?
So, your third answer and sixth answer are... (EQUAL or UNEQUAL?)
But but, that can't be! We are saying that 0.333... multiplied by 3 =
Isn't that AMAZING?

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0.999... The Truth! Quiz

by Bray

Created Oct 28, 2009 in Science
Game Plays 5,681

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	Bray:	Oct 28th, 2009 at 13:29 GMT		1 point
	For the second answer, I cannot accept all equivalent fractions, so I am only accepting answers with any of the three lowest possible denominators.

	Trevor:	Oct 28th, 2009 at 13:30 GMT		22 points
	Nice idea, but probably a poor proof to use. Naysayers'll probably cling to the thought that "1/3" doesn't exactly equal "0.333..." and that's it's just the closest approximation. Probably would've been better to use: x=0.999... 10x=9.999... 9x=10x-x=9.999...-0.999...=9 x=1 Thus, 0.999...=1 Ah well, though.

	rockgolf:	Oct 28th, 2009 at 13:31 GMT		12 points
	Your last answer is wrong. That's not amazing at all. But it is an elegant proof. ;) Style-wise, I recommend that you expand the width of the first column to 60%. Your instructions are much larger than your answers.

	Bray:	Oct 28th, 2009 at 13:46 GMT		2 points
	@SRG: I considered using that, but I thought this idea would be simpler for people who aren't already aware of this mathematical 'loophole'.

	Bray:	Oct 28th, 2009 at 13:47 GMT		4 points
	@rockgolf: Thank you for your feedback. I'm rather new to game creation, so I don't really understand how style works... And I'll change the answer for the last one. :)

	Bray:	Oct 28th, 2009 at 13:52 GMT		3 points
	And one more thing: any questions that can be answered 'yes' or 'no' accept both answers (as do the equal/unequal questions). It's difficult to get any of these wrong.

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	Osprey39:	Oct 29th, 2009 at 07:20 GMT		12 points
	^ The 9 is repeating, moron. They are equal. This is basic sixth grade stuff.

	yoshikatsu1508:	Oct 29th, 2009 at 10:56 GMT		2 points
	not reli sporcle stuff, but it is an interesting lesson in mathematics

	Bray:	Oct 29th, 2009 at 12:57 GMT		4 points
	@Sswan: I'm aware it's a commonly known thing, I just mad ethis so people who don't know about it can understand it ;) @Sugarpill11567: It isn't 0.999, it's 0.999 RECURRING (or 0.999...). The nines are infinite. @Osprey: Correct! @Yoshikatsu1508: Yeah, it's not really perfect for this site, I just thought it'd be an interesting idea to post this :)

	ODDO:	Oct 29th, 2009 at 16:52 GMT		19 points
	My favourite proof: if 0.999... is NOT equal to 1, then it is either greater than or less than 1. It's certainly not greater than 1, so it would have to be less than. But if it's less than 1, then we must be able to find a number between 0.9999... and 1. Which we can't. So 0.999... = 1 :)

	andrewd:	Oct 29th, 2009 at 17:49 GMT		12 points
	You should accept ".999" for the question where you want "0.999" as the 0 isn't essential (and many people don't write it)

	PublicEnemy:	Oct 29th, 2009 at 21:26 GMT		3 points
	wow the third one you actually need the elipsis? shouldn't .999 be good enough?

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	Kalessin:	Oct 30th, 2009 at 05:50 GMT		6 points
	sugarpill11567: they ARE the same. 0.999... is simply another way of writing 1. Believe us.

	rb357:	Oct 30th, 2009 at 22:08 GMT		5 points
	Sugarpill: Another sum you can do is this; x = 0.999... (infinite number of nines after the decimal point) 10x = 9.999... (again, an infinite number of nines after the decimal point) 9x = 9.999... - 0.999... 9x = 9 x = 1

	Bray:	Oct 31st, 2009 at 21:52 GMT		5 points
	Apologies about making '.999' not acceptable, I neglected that some people do not write the 0. '.999' is now acceptable, apologies for the inconvenience I suppose.

	foyherald:	Nov 2nd, 2009 at 03:10 GMT		-2 points
	All I can add is try using logarithms to find the answer to this equation '1+1 -=?' Go on I dare you!

	foyherald:	Nov 2nd, 2009 at 03:26 GMT		3 points
	13 *7 = 28 http://www.youtube.com/watch?v=Lo4NCXOX0p8

	madams:	Nov 24th, 2009 at 03:08 GMT		8 points
	I definitely did not understand that the answer to the first question was just yes. I kept trying to answer what 0.999... was. I was like umm...non terminating decimal? Oh lord...

	cocky:	Nov 26th, 2009 at 16:04 GMT		17 points
	No real comment on this quiz, but I think they should create a seperate category for math quizzes and seperate them from the science ones. Agree?

	bigbookofarbans:	Nov 28th, 2009 at 02:42 GMT		-3 points
	the 4th question should accept "1" as well as "3/3" seeing as they are the same exact thing.

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	rlnintendo:	Nov 29th, 2009 at 13:09 GMT		1 point
	i would have prefered trevors proof. thats the way i learned in school last year. (6th grade) but you way could be considered easier to understand

	rlnintendo:	Nov 29th, 2009 at 13:17 GMT		-3 points
	*your way

	Ace119:	Dec 2nd, 2009 at 04:04 GMT		1 point
	great quiz

	SamB45:	Dec 2nd, 2009 at 17:27 GMT		9 points
	I learned it as 1/9 = .111..., 2/9 = .222..., etc. up to 8/9 = .888..., so it would follow that 9/9 = .999..., but we all know that 9/9 = 1, therefore .999... = 1

	statephone:	Dec 4th, 2009 at 17:35 GMT		-1 points
	hard to wrap my brain around, but ODDO explained it in a way that made sense.

	t87:	Dec 9th, 2009 at 03:16 GMT		7 points
	hi bray, i'd like you to meet my friend, Calculus, and his son, Limits. you guys will probably make great friends.

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	nymets18:	Feb 5th, 2010 at 19:34 GMT		1 point
	Great quiz. Amazing.

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	Rifsun:	Feb 13th, 2010 at 01:51 GMT		1 point
	The way I look at it is, what is 1 - .999...? You give me a small positive number, and we can quickly see that in fact the difference is less than that. This implies 1 - .999... = 0, which in turn through basic algebra shows 1 = .999...

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	Drbling:	Feb 14th, 2010 at 22:36 GMT		-2 points
	"My favourite proof: if 0.999... is NOT equal to 1, then it is either greater than or less than 1. It's certainly not greater than 1, so it would have to be less than. But if it's less than 1, then we must be able to find a number between 0.9999... and 1. Which we can't. So 0.999... = 1 :)" This just proves that either the continuum hypothesis is wrong, or that .999 repeating is not a real number. The fact remains that for every 9 you add to the sequence you come that much closer to 1, but regardless of how many you add on there is an infinite number in between so you could never achieve the full value of 1.

	WyvernSabres:	Mar 25th, 2010 at 01:50 GMT		8 points
	@Drbling. Either argue logically or shut up! "You could 'never' achieve the full value of 1." Not in finitely many decimal places you can't, no. But 0.999... represents infinitely many decimal places, and several simple proofs have been given to show that this equals 1. There is no rounding involved, and real numbers (unlike letters of the alphabet) form a continuum, so for any two different numbers there must be another (in fact, infinitely many) numbers in between.

	JoeFish:	Apr 6th, 2010 at 05:29 GMT		5 points
	But of course, Drbling, we know that both the continuum hypothesis and the rejection of the continuum hypothesis are both consistent with the most commonly accepted set of mathematical axioms (ZFC). This doesn't figure into the argument at all, though, because the real numbers are defined in such a way that any two numbers define either a point (if they're the same) or a dense interval (if they're not the same). By the definition of, well, numbers, if you can't find a number between .999 repeating and 1, they are the same number. If you do find one, get back to us and we'll give you the Fields' Medal. Or a cookie.