harry42
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What is -0.5 rounded to the nearest whole number?
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Maths question
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SS4
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The set of whole numbers isn't well defined mathematically but I would say it's the same as the set of integers.
Rounding rules dictate it is rounded up because 0 > -1
Qwerty133
Established Member
-1 looking at Wikipedia who use the example of -23.5 which is rounded down to -24
hairyhandedfool
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There are no set rules for rounding unless preference is specified in the particular query. The most common rules are:
Rounding Up (0)
Rounding Down (-1)
Rounding Towards zero (0)
Rounding away from zero (-1)
At school I was always taught to 'Round up'.
Rounding Up (0)
Rounding Down (-1)
Rounding Towards zero (0)
Rounding away from zero (-1)
At school I was always taught to 'Round up'.
nathanclass323
Member
-1 is the nearest WHOLE number.
asylumxl
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It is rounded to -1.
deltic
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my initial thought would be to round up to 0 but as I would round -1.5 to -2, so I would have to agree you should round to -1. Excell rounds to -1
edwin_m
Veteran Member
Another option is to round halves to the nearest even number, which would give zero. This can be useful if the numbers are later averaged, since the average of the rounded numbers will be closer to the average of the originals.
David Goddard
Established Member
The answer would be -1. The sign is irrelevant in these cases.
zero isn't an even number. An even number is a number that can be split evenly by 2. Zero can not be divided by 2.
TheKnightWho
Established Member
Yes it is! Don't confuse 0 with 'nothing'. There're whole books written on things like this
bb21
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Zero is most definitely even.
By your own definition: 0 ÷ 2 = 0 with no remainder, hence zero is even.
The question in the OP is meaningless without context. Both zero and -1 are correct. Neither is closer to -0.5 than the other. It comes down to common practice. With positive numbers, common practice is rounding halves up, but there is no such thing for negative numbers AFAIK so both can be the correct answer.
I am surprised that so many people are sure that the answer is -1 and not 0.
Yes it is! Don't confuse 0 with 'nothing'. There're whole books written on things like this
your both incorrect, zero is not an even number. I will provide supporting evidence when I am at my laptop rather than my phone, you can not divide zero by any number. Go stick zero divide by any number into excel or a scientific calculator you will get a !div0! Error.
(I am currently studying a maths degree and the module currently working goes into extensive detail why zero is not an even number and also why zero cannot be divided by any number)
Searle
Established Member
Would just like to point out that excel proves that the algorithms used behind Excel prove/disprove something, it's not a way of proving something is/isn't right
0 / x = 0, if x != 0.
Excel or a scientific calculator will give this result, although that doesn't prove anything, of course.
Are you thinking of *dividing* by zero? That indeed gives an undefined result.
edwin_m
Veteran Member
Wrong way round. You can't divide anything by zero but you can divide zero by anything.
hairyhandedfool
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Tell me something, which came first, maths? Or Excel/scientific calculators?
Absolutely. If you had a cake and no-one wanted any you'd be left with a cake (one divided by zero equals one????). If 5 people wanted cake but no-one had baked one, none of the five would get any (zero divided by five equals zero).
edwin_m
Veteran Member
Mmmm, a cake post! Can I have it and eat it too?
Actually, both Excel and calculators will allow zero to be divided by something. The DIV/0 error arises only when dividing by zero.
TheKnightWho
Established Member
Forgive me if I'm a little sceptical, as I was myself doing a maths degree for a while before I decided to change to something else. I haven't heard of anyone saying that you can't divide 0 by anything, but anything divided by 0 is undefined.
It's the difference between 0 and NULL in C++, for example.
I split the decimal places up evenly so
0.0 to 0.4 (5 decimal places) get rounded down (to 0)
0.5 to 0.9 (5 decimal places) gets rounded up (to 1)
Because -0.5 is below zero then it becomes
0.0 to -0.4 gets rounded up (to 0)
0.5 to 0.9 gets rounded down (to -1)
Its all a question of trying to keep things averaged as evenly as possible.
0.0 to 0.4 (5 decimal places) get rounded down (to 0)
0.5 to 0.9 (5 decimal places) gets rounded up (to 1)
Because -0.5 is below zero then it becomes
0.0 to -0.4 gets rounded up (to 0)
0.5 to 0.9 gets rounded down (to -1)
Its all a question of trying to keep things averaged as evenly as possible.
SS4
Established Member
Can we use RMS instead? 
From my Degree text book:
I have read on a bit since my previous post, and now found it is highly disputed whether zero is odd or even, the text book gives both arguments. Its argued it is even because splitting 0 between 2 they both get zero. The other side uses the cake example that if you have no cake you cant split it between two people as there is nothing to split so therefore can not possibly be even, as to be even 2 people should both get a portion.
, for example if you were decorating and need 7.2 rolls of wallpaper you'd round this up. If you were measuring for how many cupboards would fit along a wall, and you came out with 7.8 you'd round to 7 as 8 will not fit. This applies to positive and negative numbers so there is no correct answer without context.
I have read on a bit since my previous post, and now found it is highly disputed whether zero is odd or even, the text book gives both arguments. Its argued it is even because splitting 0 between 2 they both get zero. The other side uses the cake example that if you have no cake you cant split it between two people as there is nothing to split so therefore can not possibly be even, as to be even 2 people should both get a portion.
For the purposes of rounding .5 to the nearest even number, treating zero as even is required if the context is to ensure that the rounding errors statistically cancel out over a large set of linearly distributed data (which is usually the reason for choosing to round to nearest even number).
Whether it's treated as even in other contexts doesn't really matter.
--- old post above --- --- new post below ---
Statistically, that method will give an always increasing cumulative rounding error, as it's incorrect to include 0.0 in the set. There's essentially 4 cases:
.00 - no rounding required
.01 to .49 - round towards 0
.50 - round towards even
.51 to .99 - round away from 0
I used 2 decimal places there, as it sometimes helps to look at it that way.
As previously stated, however, context is everything, that's just a useful default way of handing data which often eliminates cumulative error.
Whether it's treated as even in other contexts doesn't really matter.
--- old post above --- --- new post below ---
Statistically, that method will give an always increasing cumulative rounding error, as it's incorrect to include 0.0 in the set. There's essentially 4 cases:
.00 - no rounding required
.01 to .49 - round towards 0
.50 - round towards even
.51 to .99 - round away from 0
I used 2 decimal places there, as it sometimes helps to look at it that way.
As previously stated, however, context is everything, that's just a useful default way of handing data which often eliminates cumulative error.
Rounding has conventionally been always to the modulus of the number.
Ie you ignore totally whether the number is negative or positive.
So rounding a negative number yields the same output value as rounding the equivalent positive number, but negative.
This also means that rounding up -0.5 gives an answer of -1, rather counter intuitively.
Another way of looking at this is that rounding up means moving away from zero, rounding down means moving towards zero.
Ie you ignore totally whether the number is negative or positive.
So rounding a negative number yields the same output value as rounding the equivalent positive number, but negative.
This also means that rounding up -0.5 gives an answer of -1, rather counter intuitively.
Another way of looking at this is that rounding up means moving away from zero, rounding down means moving towards zero.
PaxVobiscum
Established Member
How typical of these forums - someone asks a reasonable question and in no time we're arguing about nothing!
It's not highly disputed. You are the only one claiming it is not even. The rest of the world looks to see if there is any remainder after dividing by 2, and if not then it is even.
As mentioned I am quoting a degree level text book. there is nothing to divide by 2,
For cakes, maybe, but for numbers, 0/x = 0, for all x != 0. Or, if you really don't like seeing it written that way, 0 * 1/x = 0 for all x != 0. You really don't need a degree level text book for that.
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