What does 0.4999... round to?

[The Green Bean]

Originally posted by: AccruedExpenditure
it's 0.

 

[sadffffff]

to review:
.999...=x
9.999...=10x
9=9x
1=x

similarly:
.4999...=x
4.999...=10x
4.5=9x
.5=x

since .4999... IS .5 and we are rounding to the nearest whole .4999... rounds to 1

 

[destrekor]

Originally posted by: sadffffff
to review:
.999...=x
9.999...=10x
9=9x
1=x

similarly:
.4999...=x
4.999...=10x
4.5=9x
.5=x

since .4999... IS .5 and we are rounding to the nearest whole .4999... rounds to 1

general rule of thumb is to only round once in order to keep the answer more accurate.
more accurate, in the long run, is .499 is closer to 0, no if's ands or buts. should it round one way or the other matters not when mathematically you cannot deny it is closer to one side or the other. that's like being on the line but not centered on the line and barely oh barely more on one side than the other side just because you are not exactly center on that line, as if a laser is measuring you. can't comprehend the distance in our heads, but math can. because math is smart like that.

 

[Suspicious-Teach8788]

Originally posted by: Dritnul

Originally posted by: Leros

Originally posted by: Dritnul

Originally posted by: clickynext
Exactly 5 is the only point of vagueness. 0.4999 clearly rounds to 0 because it is still infinitesimally closer to 0. At 5, you could go either way and it's just convention to round up.

ur in the boat with me man i dunno if its cuz i think like a scientist or i don't smoke enough pot but theres no way they gonna see the light

0.4999 does indeed round to 0.

We are talking about 0.4999...... with infinitely many 9's.

Think about this:
1 - 0.9 = 0.1
1 - 0.99 = .01
1 - 0.999 = .001
What happens if you have an infinite number of 9's?
You get an infinite number of 0's.
1 - 0.999999........ = 0.00000000000.......... = 0
Therefore: 1 = .99999..........

In the same way:
0.5 - 0.49 = .01
0.5 - 0.499 = .001
0.5 - 0.4999 = .0001
What happens if you have an infinite number of 9s?
You get an infinite number of 0's.
0.5 - 0.49999........ = 0.0000000000 = 0
Therefore: 0.5 = 0.49999........

again i still think its a limit it never actually is .5 although .4999999..... is infinitely close to .5 it never exactly equals it

last time ill say it for tonight
good-night ATOT

Wrong. Using a limit view implies TRUNCATION of the 9s. There is no truncation infinite 9s = 0.5. QED.

Try to prove me wrong without truncating any 9s. If you end up doing so, I'll give you a cookie. But otherwise, all these counterproofs are flawed.

 

[thesurge]

Originally posted by: iamaelephant

Originally posted by: Tiamat
0.4999... is 0.500... for all intents and purposes.

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.

If we leave an Archimidean field/ring with non-zero infinitesimals, then your statement is incorrect.

But for regular stuff, .49999....=5

 

[DrPizza]

Originally posted by: Dritnul
I would think that any calculus teacher would tell you that .49repeting =/= .5 it would probly be one of those limit problems where the number gets infinitely close to .5 but never touches it

that would be the calculus perspective that's the perspective i'll take i guess

I *AM* a calculus teacher, and I'll tell you that you're wrong. There is absolutely no rounding or limit involved. .49999... EQUALS EXACTLY .5

Now, about rounding it:

Although it is customary to round the number 4.5 up to 5, in fact 4.5 is no nearer to 5 than it is to 4 (it is 0.5 away from either). When dealing with large sets of scientific or statistical data, where trends are important, traditional rounding on average biases the data upwards slightly. Over a large set of data, or when many subsequent rounding operations are performed as in digital signal processing, the round-to-even rule tends to reduce the total rounding error, with (on average) an equal portion of numbers rounding up as rounding down. This generally reduces the upwards skewing of the result.

 

[Schfifty Five]

People who say there are two roundings are wrong. There is only one rounding.

0.49999....(repeating) = 0.5, so you're just rounding once to 1.0

 

[Spacehead]

For my simplistic uses, i would round 0.4999... to 0

 

[brandonbull]

Originally posted by: Turin39789
please discuss practical applications of this argument

Mathematics' version of Jeopardy.

"The answer .9999 = 1"
"What is the Bleepenhymer-Frazzlevich-Hoffenpheffer theorem"

 

[BrokenVisage]

For all intensive purposes.. who cares anymore?!

 

[xtknight]

Where's the option for 'unreal answer'?

 

[AnandTech Moderator]

Meh. I was going to lock this but it's too much fun watching some of you make fools of yourself.

 

[JoeFahey]

Originally posted by: AnandTech Moderator
Meh. I was going to lock this but it's too much fun watching some of you make fools of yourself.

:thumbsup:

 

[spidey07]

Originally posted by: AnandTech Moderator
Meh. I was going to lock this but it's too much fun watching some of you make fools of yourself.

Indeed. Teh math is not strong with many people.

 

[Born2bwire]

Originally posted by: AnandTech Moderator
Meh. I was going to lock this but it's too much fun watching some of you make fools of yourself.

When will the hurting stop?

 

[Ayah]

My head hurts. I say we flip a coin.

 

[Furyline]

0.4999... = 0.5 I would round it up to 1

1/90 = 0.0111...
40/90 + 5/90 = 0.4444... + 0.0555... = 0.4999...
40/90 + 5/90 = 45/90 = 1/2 = 0.5
0.4999... = 0.5

 

[yosuke188]

You round to 1. Anyone who argues otherwise is dumb.

 

[Dritnul]

if you round to one you round to the ones place so only the one/tenths place matters so for rounding purposes .4=.45=.49=.49999=.49999... and they all round to zero

and since this is making less progress than a debate on which religion is correct im moving on to other threads

 

[DrPizza]

lmao at Dritnul's choice of sig! Uhhh, Dritnul, the Anandtech Moderator was talking about you, not siding with you.

and, one more time:

You round to 1. Anyone who argues otherwise is dumb.

I'll argue that you round to 0 in many situations.

When dealing with large sets of scientific or statistical data, where trends are important, traditional rounding on average biases the data upwards slightly. Over a large set of data, or when many subsequent rounding operations are performed as in digital signal processing, the round-to-even rule tends to reduce the total rounding error, with (on average) an equal portion of numbers rounding up as rounding down. This generally reduces the upwards skewing of the result.

Hence the rule: "round to even" Google it.

 

[Dritnul]

Originally posted by: DrPizza
lmao at Dritnul's choice of sig! Uhhh, Dritnul, the Anandtech Moderator was talking about you, not siding with you.

not just me i just seem to be the main target cuz ive posted the most anyways on to another thread

 

[neit]

I guess I'm on the fence here, but i voted option 2. basically i see it in engineering terms, if i do a calculation that only allows me one significant figure (which is why you'd round), then the .4 would round down to 0, since the closest certainty is you have is that you're less than 0.5.

if you're looking at it from a mathematical perspective and just looking at the numbers and not the context, then iirc .4999(9 repeating) is .5, and hence would only round once to 1.

 

[iamaelephant]

Originally posted by: destrekor

Originally posted by: sadffffff
to review:
.999...=x
9.999...=10x
9=9x
1=x

similarly:
.4999...=x
4.999...=10x
4.5=9x
.5=x

since .4999... IS .5 and we are rounding to the nearest whole .4999... rounds to 1

general rule of thumb is to only round once in order to keep the answer more accurate.
more accurate, in the long run, is .499 is closer to 0, no if's ands or buts. should it round one way or the other matters not when mathematically you cannot deny it is closer to one side or the other. that's like being on the line but not centered on the line and barely oh barely more on one side than the other side just because you are not exactly center on that line, as if a laser is measuring you. can't comprehend the distance in our heads, but math can. because math is smart like that.

We're not talking about 0.499, we are talking about 0.4999.... (infinitely repeating 9's). So you're wrong.

 

[episodic]

I told my 7th grade son that .99 repeating = 1. He argued for a moment, then I explained it to him - he thought a moment, and said - hey that makes sense.

 

[funboy6942]

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