I believe .999... = 1 like any sane person does (uh-oh), but I'm not really sure where to go with this one. On the one hand it technically is equal to .5 which rounds to 1, but if it's just ever so smaller than .5, which could also be the case, then it'd be 0..
What does 0.4999... round to?
- Thread starter Syringer
- Start date
novasatori
Diamond Member
- Feb 27, 2003
- 3,851
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You don't just round numbers to whatever you feel like. You have to set a standard; round to the nearest ones place or round to the nearest one hundredths place.
Originally posted by: mugs
Ok, let me get this straight...
You believe .999... = 1 like any sane person does
You believe that .4999... "technically" = .5
And yet you think .4999... is smaller than .5
...
Well, there is a branch of mathematics which would say that you can have two real numbers be simultaneously equal and inequal. It's all in how you define things.
The concept of rounding arises naturally out of mathematics, but the supposition that numbers exactly halfway between sucessive integers get rounded up is about as arbitrary and unnatural as you can get.
Do you not know what the "=" sign means? It mean EQUALS, meaning that 0.499... is EXACTLY THE SAME NUMBER as 0.5, so why would it round to anyone other than what 0.5 rounds to, ie 1. Anyone with half a brain knows that if 0.999...=1 then 0.4999 rounds to 1.
He speaks the truth.
0.4999... is not any amount smaller than .5. If .5 rounds up to 1, then any other number that is EQUAL must also round to 1.
For rounding digits whose value is 5, I believe the convention is to round up if the preceding digit is odd and round down if it's even. e.g. 0.5775 to 3 sig. digits would be 0.578 while 0.5765 would be 0.576.
So if you consider 0 to be even (it certainly isn't odd), then 0.5 ~= 0.
So if you consider 0 to be even (it certainly isn't odd), then 0.5 ~= 0.
0.4999... is 0.500... for all intents and purposes. If you consider zero an even decimal, then you round down. Therefore, 0.49999... or 0.5000... is equivalent to zero upon rounding. This method is used when you are dealing with a data set in which you are making judgements based on statistics.
If you want to do it the "grade-school" way, always round up.
Howard beat me.
If you want to do it the "grade-school" way, always round up.
Howard beat me.
People have to stop making that mistake. Please don't qualify that statement with "for all intents and purposes." 0.4999... is 0.5. End of story.
I used the phrase because I wasnt sure if using the elipses was good enough for this crowd, or if I had to actually spell out trailing 9's. (Usually I use the bar over the 9's but I dunno how to do this in html).
Also, .4999... = 0.500... not just 0.5. The trailling 9's notation I used denotes infinite significant figures, so, its equivalent has to also have infinite significant figures.
but saying that it equals .5 which equals one is rounding twice which kinda makes rounding extremely vague
IAteYourMother
Lifer
- Nov 3, 2004
- 10,491
- 22
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well hell i mean with the logic in this thread ......
.226 rounds to .25 which rounds to .5 which rounds to 1
therefore .226=1
.226 rounds to .25 which rounds to .5 which rounds to 1
therefore .226=1
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