However I'm pretty sure "greatest" refers to the magnitude of the number and is nothing to do with its direction. So it should be -8 as that makes the number have the greatest modulus.
@@NeonSqueaky in negative integers rounding up means rounding up to the number nearest to 1 as it will be greater . So in this case -7 is the answer because -7 is greater than -8 and -7 is the nearest to 1. And in case of negative integers the magnitude of a number is determined by the - sign .
@@ca-ke9493 shouldn't that mean it should be rounded to -7. See 7.4 is rounded to 7, 7.49 is rounded to 7 and then bam 7.5 is rounded to 8. So in a similar order -7.6 is rounded to -8. -7.51 is rounded to -8. But then bam -7.5 is rounded to -7
@@varunkachroo3400 you are bringing up a important point which is that, the number we round to is completely arbitrary. It’s just a convention we created, but rounding either way is equivalent.
@@jhoanoffyes you can round towards infinity, towards negative infinity, towards zero, away from zero, towards even, and towards odd. It’s most common to round towards infinity, but many people especially in statistics round towards even so there isn’t artificial bias towards infinity in a dataset
According to “bankers’ rounding” we round to the even integer when the number is exactly halfway between two integers. So, -7.5 rounded to the nearest integer is -8.
-8 It's a greater value despite being farther away from positive. If someone was running to the left at 7.5 meters per second that would round to 8 even if it was in the negative direction.
It would 100% be -8. The reason it's customary to round up when it's 0.5 is because if there are any numbers after the 5, it's now closer to the higher (or lower, in the case of negative numbers like these) number. Sometimes, if it's exactly half, mathematicians will round to the nearest even number, so either way it's always -8.
The reason it's -8 is because the negative sign just means it's multiplied by -1. In other words, it's just 7.5 * -1, but round 7.5 first to be 8, and it would be 8 * -1 which is -8. Significant figures suck😅
However I'm pretty sure "greatest" refers to the magnitude of the number and is nothing to do with its direction. So it should be -8 as that makes the number have the greatest modulus.
@lolpol-hn8dv Yes, there is. The concept of direction and magnitude of numbers is very much a thing in higher levels of maths with the modulus and argument functions of numbers. Whilst this is typically applied to complex numbers with an imaginary part, it is also applicable to those within the real subset of the complex numbers.
@@lolpol-hn8dv Haha yup, also got stuck on his wordings "Magnitude" and "direction" like there aren't two options😅😅 Maybe hes done some physics lately and it stuck, who knows🤷♀️
(Maths teacher) okay so a ‘whole number’ and an ‘integer’ are not the same thing. Whole numbers are non-negative integers. So the answer would be 0. If you wanted it to the nearest integer rounding convention dictates you round it to -8. Think of it like this. If -7.5 had been cut off and was -7.50000000…1 would it in fact be closer to -7 or -8? -8
Aaaaahhhhh! My instinct was sure of the opposite but yes! That makes so much sense. Being asked questions is so helpful. Please teach me maths! Do you do tutoring? 😊
The term 'whole number' is ambiguous, and it CAN mean integer. It's like the set of natural numbers, which can either contain zero or not, it depends on the author in most cases. And rounding is ambiguous, too, in this situation. In the most widespread interpretation, the result would be -8, but this is one of the rare cases in maths where there is room for interpretation. (Maths teacher)
I think it would be -8 because the point of rounding is to add basically to the start of your answer (ex: 1.9 is BASICALLY 2) to simplify it. And since you round up with 5 where I come from, I’d say -7.5 is basically -8
When rounding -7.5 to the nearest integer, we round to the nearest whole number. Since -7.5 is halfway between -7 and -8, the rounding convention is to round to the even number, making it -8. This is known as "round half to even" or "bankers' rounding."
that’s only one rounding convention though there’s also round half to odd, round half toward zero, and round half away from zero (which is what is typically used, and would also make the answer here -8)
It all depends on the rounding rule you use. I prescribe for the round away from zero which makes it consistent and unbiased. Either way ask the person grading your work that's what matters.
-8. Significant figures rules. Rounding off a number that is exactly 5 at the end has 2 outcomes. If the number before it is even, round off to the previous number. Eg. 9.45 ~ 9.4 If it's odd, round off to next number Eg. 9.15 ~ 9.2 Hence in -7.5, 7 is odd, so answer is rounded off to next number -8.
-8. I think rounding 7.5 up sort of makes sense if you consider that if there was any digit after the 5, it would be closer to 8 - so doing it that way is important when you round a number with a lot of digits and aren't considering the digits that come later. So, to keep it the same, 7.5 rounded is 8 and -7.5 rounded is -8.
If you’re rounding to the nearest integer, I think for consistency sake it needs to be -8. If you think of it in sort of like a form like this (I don’t have squiggly equals) 7.5=8 -> -7.5=-8. I think it’s easier to have more of a distance from zero type rule like this since it specifies to the nearest integer
When rounding -7.5 to the nearest integer, we follow the convention that if the decimal part is exactly halfway between two integers, we round to the nearest even integer. In this case, -7.5 is equidistant from -7 and -8. Since -8 is even, we round to -8 I think....!
The answer is -7 because when we roun off to the nearest integer , we choose the greater number as we are supposed to go towards the right on the number line . In this case -7 is greater than -8 as it lies towards right on the number line and claser to zero . Just remember that we have to go towards the right, and you'll get the answer!!
It is not the nearest “greatest” number. It is the nearest WHOLE number and therefore -8. If you think of rounding to the hundredths place you’ll see it doesn’t matter it is negative eg. -7.145 -> -7.15 (A college senior math major)
Idk what kind of math major you are, I'm 17 and even I know that -8 isn't a whole number, it's an integer. Also, you can't throw out the "greatest" part or there's no longer any convention to which number is closer to 7.5. 7 and 8 are both 0.5 away from 7.5 so no. Rounded up := celing function Rounded up(-7.5) := ceil(-7.5) = -7
@@pedrosso0thank you, a lot of people seem to be confused about the difference between integers and whole numbers, it doesn’t help that even the question is wrong and refers to them as being the same thing
I think it is -8 Cuz when the digit to be rounded is halfway (i.e, 7.5) and 5 is digit to be eliminated, we tend to consider if the digit before 5 is odd or even. In this case, since it happens to be odd(7) The digit is raised by 1 to make it even= (-8) However, if that digit was even eg : (8.5), then the 5 would be eliminated without any changes in the even digit=(8) What I am confused is why they mentioned (whole no.) in the brackets when -8 is an integer?
Nothing says the rule get reversed if the number is negative. if the definition doesn't specify a special case for negative number (in this case the rule is "rule is reversed" and special case is "negative number") then it means the definition has already account for all the special cases including negative numbers
-7.5 rounds to -8 because 7.5… rounds to 8 since it’s based on only the next digit. That way you know numbers barely closer to 8 than 7-7.51, 7.58, 7.5006, etc.-round to 8 without checking any digit beyond the 5. For the same reason -7.5 rounds to -8 so that you know -7.53, -7.50009, etc. round to -8 just by checking up to the 5 in -7.5…
The answer is -7 as we should always round up to the next greatest no. Which is available If we have -0.5 as an example 0 will be the answer. Likewise for every negative number the lesser -ve value is the greatest. Edit:but do checkout the question because it is written whole number in the bracket which seems to not be in the ground of the question as whole numbers do not contain -ve integers. But according to chatgpt it says the -ve numbers should be rounded away from 0. So I was wrong. The answer is -8. I read phd level maths article for this question and still the answer is -8..yay!! I learnt something new today🎉😂
SHE’S TAKEN AT LEAST 2 LINEAR ALGEBRA COURSES AND A LEVELS LINEAR ALGEBRA AND IS STILL HARDCORE CONFUSED ABOUT WHAT IT MEANS FOR A SPACETIME VECTOR TO BE TIMELIKE
actually i usually repeatedly watch your all videos i love your oxford university journey i miss all of your old videos 😢(take love from Bangladesh lucy dear)
it would be to -8 because of situations when we don't know the digits afterwards. For example -7.5 and -7.50001 round to the same whole number, but we know that -7.50001 is closer to -8. This is also the reason why we round 7.5 to 8.
As a high school student using [-7.5] or finding it's greatest integer function would be done like -8+0.5 where the whole number part is GI i.e.-8, and {-7.5} would be .5 Hence -8 is your answer
It's wrong to say that when it's half way you always round up. Actually there's a concept called significant figures and in that there are even more detailed rules to round numbers and according to it, if the digit preceding 5 is odd, then you round it up BUT if the number preceding 5 is even then you leave it as it is. Eg- 3.5------> 4 4.5------->4 So by that logic, -7.5 should be rounded off to -8 Hope this helps
I believe The general rule of thumb is anything from 0.49(not getting too technical) is rounded down, anything from exactly 0.5 is rounded up. So 1.5 rounded to the nearest integer, would be 2. 1.4 would be 1.
I see where everyone is coming from, but I believe it should be -7 in order to conserve important properties of the round function, in particular 「round(x+n) = round(x) + n (where n is an integer)」
If you were to round up a two-digit number in this case, the decimal range would be [-6.50; -7.49] to round up to -7, putting 100 numbers inside. Beyond -7.5, this would be -8
The reason you round up is because when you reach the halfway point between the two numbers, you consider the second to be the nearest. You’re not rounding up on a positive scale, but rather increasing the absolute value, do it would be -8
There are different systems of rounding. In Java and JavaScript, rounding the number would give -7. I personally think it’s -8. It’s something to think about when dealing with these different systems. The programming languages add 1/2 then take the floor (rounds downs) which means it takes the nearest greatest number.
So -7.9 would round to -7? That doesn’t make sense. Just think of it in absolute terms. What would you do if it was positive? Round it to 8. In order to maintain the equality on the opposite side of 0, it’d have to round to -8
Think about it like a hole. If you dig "7.5" out of the ground and put it in a pile, that is a measurable amount. There is equally as much removed (negative) from the ground as there is added (positive) to the pile. And if you round 7.5 up to 8, if you make your pile bigger, in order to maintain the equality between the dirt removed from the ground and the amount in the pile, the hole becomes larger, thus more negative, therefore -7.5 rounds to -8. Plz pin this bc I like my math explanations...👀
-8 makes the most sense to me since I perceive the xy plane directionally. So x = 0 is like a mirror and negative integers and positive integers move way from each other. I don’t imagine the x plane as a continuous left to right progression of numbers (even though it is), it just made a lot more sense to me for everything negative to be right to left.
i like to think that, as 5 rounds to the furthest extremity to the right (i.e. it is closer to 10 than 0), as -7.5, -7.6, -7.7 and so on, means that -7.5 would round to -8 i think this calls into question the definition of the rule: what is meant by “greatest number”? the largest quantitative value (+ > -) or the larger number on a scale of 0.0 to 1.0 the former interpretation would lead to A, but the latter would lead to B this is interesting!
@@tinkvaternjak9311 and who mentioned natural number here? It's an integer. Integers work with modulus, regardless of the sign before it. It's still an integer.
@@saharaliake8970Integers are not the same as whole number, so the question is either wrong or the answer should be zero. Since both the options do not represent a whole number
@@mayureshchaudhary8238 yeah but the statement of whole number is in brackets so the priority is the word integers not whole numbers. You should process integers. That's subsidiary info.
For example, let's consider the number -2.2. If we need to round this number, we compare it to the value -2.5. Since -2.2 is greater than -2.5, it rounds up and the result is -2. On the other hand, if we have -2.7 and need to round it, we compare it to -2.5.
Some science disciplines say that when rounding a 5 you round not up but to the nearest even number to avoid a slight upwards skew. In this case, i would round to -8 because it is the nearest even integer. If choosing not to use this rule with the rest of your rounding however, i would round up to -7
The two most common ways to round are to round ties away from zero or to round ties up (towards pos. inf). ...So it's either -7 or -8, your choice, or somebody else's but it's a choice.
Depends on the situation. If it’s half a cent of debt to a bank, they would definitely round to more debt. Some might think of -7.5 as just 0 - 7.5, in which case you would round to 8, but if you treat a negative number as a value itself, you might round to -7. I would round to -8 because I believe that a negative number is just subracting a positive (two reasons, 1: i can’t imagine an inherently negative value, 2: negative and positive numbers are treated differently [-7x-7=49, 7x7=49])
-8 is the only answer that is consistent. Imagine you had a set of equations that included negative signs (enthalpy perhaps). For example x = -7.5 y =-x. Then y = 7.5. Say you round x to the nearest integer by going up, you get -7. Now say instead you rounded y by that method you get 8. Now y=-x and you have an inconsistency. This is solved by rounding -7.5 to -8. This should be obvious to anyone who uses mathematics on a regular basis.
I basically see as moving away from 0. So 0.5 whether positive or negative or negative would move away from 0. While 0.4 whether positive or negative would move towards 0.
In programming, the language Python rounds to the nearest even number (which seems like a very strange system) while Java adds 0.5 and then runs floor() Python’s approach seems crazy, so I’ll go with the Java approach of always rounding 0.5 to the larger (more positive) number.
-7 because when it comes units and measurements in physics, in our book their is a rule for rounding off digits, that if the number after digit is 5 then the number before is remained unchanged
i think -8, because if you extend that decision to all negative numbers, when you have -0.5 your choices are 0 and -1. zero has several properties that make it hard to work with, so it makes more sense to round it to one. (i know one has it's own issues but at least you can divide with it and multiply without eliminating everything.)
I would say -8 because you round up to the number that would have the greatest “effect”. We do this because it is usually better to overestimate something than underestimate it
The answer: it depends on context. In a data science context, rounding up away from zero (so -8) has a nice impact because on average the rounding cancels out, assuming the distribution is fairly distributed. Granted, in a language like Python, this isn’t the case, and rounding up always goes toward positive infinity. Why? Because that’s how the programmers wrote it, and it works well enough that people will just find a different solution if it doesn’t work in their context. Mathematics is about discovering a lot of fantastic things, using human defined tools. The human defined part is important here, so really it doesn’t matter which way you go, as long as you’re following a clear convention
I think I have the right answer! If it's a vector then you should round it to -8 because the negative sign only indicates direction. It doesn't indicate any special properties about the unit so if you ever converted it into its absolute value, you would round it from 7.5 to 8. If it's a scalar then it just depends on the context. For example temperature has negative values but if you're working with degrees in celsius then you have to remember that -7.5 degrees in celsius is going to be a positive number in Kelvin and I don't even want to talk about Fahrenheit. The easy solution is to just convert everything to Kelvin then do the maths that way unless for some reason it's super important to measure things with respect to freezing or boiling temperatures of water. Then celsius might be more appropriate and I think in that case they should be treated as vectors and rounded as absolute values. There are other cases such as with distance or voltage where a positive or negative value is purely based on the starting point/point of reference. Is completely arbitrary. At the end of the day, if you ever have to resort to rounding then you're not really doing theoretical maths anymore. You're probably doing engineering and in that case, the correct answer is to trial and error both options and go with whatever one works the best. Although it's probably not important anyway.
I use the rounding system my chemistry professor taught me, basically round to the nearest even number… so we’re not always consistently rounding up, making things greater than they should be
Except that’s only one of six commonly-accepted deterministic ways of rounding, especially when the fractional component is exactly 1/2. There’s nothing strictly forcing you to use the GIF, as you could opt for: - Using the LIF (LIF(x) = n, where n - 1
I mean… rounding is subjective to the situation. As an exact middle ground (7.5) you could go either to 8 or to 7 depending on what the situation is. If you assume rounding up for positive numbers (away from 0) you should do the same for negative numbers - go away from 0.
it’s -8 so that it is balanced -7.0,-7.1,-7.2,-7.3,-7.4 -> -7 -7.5,-7.6,-7.7,-7,8,-7.9 -> -8 If u round -7.5 to -7, it means there’s almost always biased towards -7 when rounding from somewhere between -7 and -8 when it should be exactly balanced if it’s random. The only time it doesn’t matter is when they’re real numbers and then (-7.5,-7] and [-7.5,-7] have the same size as the other half. But real numbers don’t exist in reality
It will be -7 I think cuz it's the nearest greatest number
However I'm pretty sure "greatest" refers to the magnitude of the number and is nothing to do with its direction. So it should be -8 as that makes the number have the greatest modulus.
@@NeonSqueaky in negative integers rounding up means rounding up to the number nearest to 1 as it will be greater . So in this case -7 is the answer because -7 is greater than -8 and -7 is the nearest to 1. And in case of negative integers the magnitude of a number is determined by the - sign .
SHE DOESNT UNDERSTAND WHAT IT MEANS FOR A BASIS TO BE ORTHONORMAL
SHE DOESNT UNDERSTAND HOW TO USE CHARACTERISTICS
exactlyyyy!!! it is not dependent on direction rather on magnitude!!!
i like the academic side of you, you should make more academic content, yk like videos where we can see your approach on questions/the way you think
-7 ❤ answer
SHE CANT SOLVE A FUCKING CAUCHY PROBLEM WHEN ITS CALLED ‘QUANTUM THEORY’
I would just consider the number in absolute terms whenever rounding, so i would say -8.
Yeah same
Why would you consider it in absolute terms?
If u think about it, -7.6 would be rounded to -8, -7.51 would be rounded to -8, so -7.5 should be rounded to -8.
@@ca-ke9493 shouldn't that mean it should be rounded to -7. See 7.4 is rounded to 7, 7.49 is rounded to 7 and then bam 7.5 is rounded to 8. So in a similar order -7.6 is rounded to -8. -7.51 is rounded to -8. But then bam -7.5 is rounded to -7
@@varunkachroo3400 you are bringing up a important point which is that, the number we round to is completely arbitrary. It’s just a convention we created, but rounding either way is equivalent.
Depends on what rounding system you are using
SHE DOESNT KNOW THE DEFINITION OF AN INTEGRAL
My thought too, in chemistry it'd be the 8 no question
THERES MORE THAN ONE ROUNDING SYSTEM?? 😵💫
@@jhoanoffyep🤔
@@jhoanoffyes you can round towards infinity, towards negative infinity, towards zero, away from zero, towards even, and towards odd. It’s most common to round towards infinity, but many people especially in statistics round towards even so there isn’t artificial bias towards infinity in a dataset
According to “bankers’ rounding” we round to the even integer when the number is exactly halfway between two integers. So, -7.5 rounded to the nearest integer is -8.
is it applicable for negative integers tho?
Yes, this is a good way of doing it because if you change the number of significant figures, then errors don’t “propagate” the same way!
Yup! I agree too, learned this in physics class for sig figs XD
So -6.5 goes to -6? That is an interesting take
this
-8
It's a greater value despite being farther away from positive. If someone was running to the left at 7.5 meters per second that would round to 8 even if it was in the negative direction.
In this case the value has no direction therefore. -7 would be greater.
-7 would be the greater value
Do you mean greater absolute value?
only beacuse you cant run negative so its the absolute value of it which is true
@@carepackage2214You can absolutely run in the negative direction, you simply have to establish which direction is positive.
It would 100% be -8. The reason it's customary to round up when it's 0.5 is because if there are any numbers after the 5, it's now closer to the higher (or lower, in the case of negative numbers like these) number. Sometimes, if it's exactly half, mathematicians will round to the nearest even number, so either way it's always -8.
You do know that-7 is nearer to 1 than -8, right?
@@monkey.druffy9022 Cool, and?
It shld be rounded to minus 7 as there is a odd number infront of the 5 as therefore it shld be increased to -7
@@ahuman7882and… it's supposed
To be rounded to -7 not -8(simply) but it really depends, you are not completely wrong
Why it's not zero? As -8 is not a whole number, the smallest whole number close to -7.5 is zero. Why is no one talking about this?
Its -8, because what would -7.4 be then? It can't be -8.
Edit: I had to fat check it, the answer is -8.
knew it
The reason it's -8 is because the negative sign just means it's multiplied by -1. In other words, it's just 7.5 * -1, but round 7.5 first to be 8, and it would be 8 * -1 which is -8. Significant figures suck😅
I'm glad you fat checked, was worried facts would be involved
@@WaterLily_Lotus I was just making fun of the fact you said fat instead of fact, I actually agree with you
Where did you check that? I used an online rounding calculator and it says -7. Maybe it’s broken idk
Still round up, since it's the "distance" to the next number, not from zero if that makes sense
I think -7? Cuz it rounds up to the nearest greater integer?
However I'm pretty sure "greatest" refers to the magnitude of the number and is nothing to do with its direction. So it should be -8 as that makes the number have the greatest modulus.
@@NeonSqueakywtf bro this is maths not science. There is no direction or magnitude in maths integers it's simple maths.
@lolpol-hn8dv Yes, there is. The concept of direction and magnitude of numbers is very much a thing in higher levels of maths with the modulus and argument functions of numbers. Whilst this is typically applied to complex numbers with an imaginary part, it is also applicable to those within the real subset of the complex numbers.
SHE CANT USE A CONFORMAL MAP TO SOLVE A BASIC DIFFERENTIAL EQUATION
@@lolpol-hn8dv
Haha yup, also got stuck on his wordings
"Magnitude" and "direction" like there aren't two options😅😅
Maybe hes done some physics lately and it stuck, who knows🤷♀️
(Maths teacher) okay so a ‘whole number’ and an ‘integer’ are not the same thing. Whole numbers are non-negative integers. So the answer would be 0. If you wanted it to the nearest integer rounding convention dictates you round it to -8. Think of it like this. If -7.5 had been cut off and was -7.50000000…1 would it in fact be closer to -7 or -8? -8
Aaaaahhhhh! My instinct was sure of the opposite but yes! That makes so much sense. Being asked questions is so helpful. Please teach me maths! Do you do tutoring? 😊
The term 'whole number' is ambiguous, and it CAN mean integer. It's like the set of natural numbers, which can either contain zero or not, it depends on the author in most cases. And rounding is ambiguous, too, in this situation. In the most widespread interpretation, the result would be -8, but this is one of the rare cases in maths where there is room for interpretation. (Maths teacher)
@@KitaKiyonori oh thank you for your input! I feel better about my instinct :).
@laurenking9524 integers can be negative as well as positive. What they mean is natural numbers
@@laurenking9524 yes and no. Won’t take money. Just like sharing the mathematical love
I think it would be -8 because the point of rounding is to add basically to the start of your answer (ex: 1.9 is BASICALLY 2) to simplify it. And since you round up with 5 where I come from, I’d say -7.5 is basically -8
SHE COMPLETELY FORGOT HOW TO USE THE PRODUCT RULE WHILE DOING A STOKES THEOREM QUESTION
That doesn’t explain anything lol. .5 is still half way, whether magnitude or direction is what’s being rounded “up” is still ambiguous.
@@tyler-iy4jkSince -7.5 is negative, that means .5 is also a negative and since .-5 is exactly halfway so it becomes -1 because -5
@@tyler-iy4jk you round up from 5. That’s how rounding up works.
When rounding -7.5 to the nearest integer, we round to the nearest whole number. Since -7.5 is halfway between -7 and -8, the rounding convention is to round to the even number, making it -8. This is known as "round half to even" or "bankers' rounding."
So, if it was -8.5 it would be -8 again?
@@Malkinsmoth it would be -9
@@Hallo85000but 9 isn't even?
that’s only one rounding convention though
there’s also round half to odd, round half toward zero, and round half away from zero (which is what is typically used, and would also make the answer here -8)
@@Hallo85000round half away from zero is also what you used to get this answer so
It's -8 that what I've been taught in highschool idk about further math students. It might be different
It all depends on the rounding rule you use. I prescribe for the round away from zero which makes it consistent and unbiased. Either way ask the person grading your work that's what matters.
SHE CANT COMPREHEND THAT THE WEAK LAW OF LARGE NUMBERS HASNT BEEN PROVEN. IT WILL BE PROVEN MANY YEARS FROM NOW WHEN YOU GRADUATE THE SECOND GRADE
It's-7
-8.
Significant figures rules. Rounding off a number that is exactly 5 at the end has 2 outcomes. If the number before it is even, round off to the previous number.
Eg. 9.45 ~ 9.4
If it's odd, round off to next number
Eg. 9.15 ~ 9.2
Hence in -7.5, 7 is odd, so answer is rounded off to next number -8.
-8. I think rounding 7.5 up sort of makes sense if you consider that if there was any digit after the 5, it would be closer to 8 - so doing it that way is important when you round a number with a lot of digits and aren't considering the digits that come later. So, to keep it the same, 7.5 rounded is 8 and -7.5 rounded is -8.
rounding “up”, up in this case is the number that’s larger, -7.
Yes I agree! If you imagine -7.50001, you would round up to -8. I think that's the point of rounding up at .5
@@zs9851you'd round -7.6 up to -7 then? you round up for 7.5, 7.6, 7.7, etc.
@@spookyspirits4462 yes i would, -7 is larger than -8 isn’t it, so therefore you round up and to the larger number
@@zs9851you're saying you would round -7.6 to -7? you sure you read that comment correctly?
If you’re rounding to the nearest integer, I think for consistency sake it needs to be -8. If you think of it in sort of like a form like this (I don’t have squiggly equals) 7.5=8 -> -7.5=-8. I think it’s easier to have more of a distance from zero type rule like this since it specifies to the nearest integer
Nah cause ur rounding it up to the greatest no. In the first case but in the second cas ur rounding it up to a smaller no.
-8 imo. With rounding I feel like it’s more a magnitude thing if that makes any sense.
When rounding -7.5 to the nearest integer, we follow the convention that if the decimal part is exactly halfway between two integers, we round to the nearest even integer. In this case, -7.5 is equidistant from -7 and -8. Since -8 is even, we round to -8 I think....!
I never thought about this. Now MY family's divided, lol.
8. If you round both 7.5 and -7.5 you’d want the absolute value of both to be equal for consistency
The answer is -7 because when we roun off to the nearest integer , we choose the greater number as we are supposed to go towards the right on the number line . In this case -7 is greater than -8 as it lies towards right on the number line and claser to zero . Just remember that we have to go towards the right, and you'll get the answer!!
U can check google cause -.5 rounded is -1 so likeee
It is not the nearest “greatest” number. It is the nearest WHOLE number and therefore -8. If you think of rounding to the hundredths place you’ll see it doesn’t matter it is negative eg. -7.145 -> -7.15
(A college senior math major)
Idk what kind of math major you are, I'm 17 and even I know that -8 isn't a whole number, it's an integer. Also, you can't throw out the "greatest" part or there's no longer any convention to which number is closer to 7.5. 7 and 8 are both 0.5 away from 7.5 so no.
Rounded up := celing function
Rounded up(-7.5) := ceil(-7.5) = -7
@@pedrosso0thank you, a lot of people seem to be confused about the difference between integers and whole numbers, it doesn’t help that even the question is wrong and refers to them as being the same thing
I think it is -8
Cuz when the digit to be rounded is halfway (i.e, 7.5) and 5 is digit to be eliminated, we tend to consider if the digit before 5 is odd or even.
In this case, since it happens to be odd(7)
The digit is raised by 1 to make it even= (-8)
However, if that digit was even eg : (8.5), then the 5 would be eliminated without any changes in the even digit=(8)
What I am confused is why they mentioned (whole no.) in the brackets when -8 is an integer?
I've never heard of the even/odd rule for me 6.5 rounds to 7
She's right , the odd even rule is true , been taught us in 11th class
SHE DOESNT UNDERSTAND WHAT A METRIC IS IF ITS NOT THE STANDARD EUCLIDEAN METRIC
Physics class 11 good work 🎉
I would do -7 because it’s technically a bigger number
I’m on the side of -8 because the whole reason that’s the direction they decided on is that there could be something after the .5 that’s cut off.
Definitely-8 because the rule is just reversed if the number is negative
Nothing says the rule get reversed if the number is negative. if the definition doesn't specify a special case for negative number (in this case the rule is "rule is reversed" and special case is "negative number") then it means the definition has already account for all the special cases including negative numbers
It's -8 because when -7.51 would be rounded to a whole number we would round it to -8 as well because thats closer than -7.
I would really love more of like these videos your thinking is similar to mine and it makes me feel understood in some kind of way
-7,plus pllzzzz make long videossssss,i really miss them
SHE DOESNT UNDERSTAND THE COMPLEX NUMBERS IS A GROUP
-7.5 rounds to -8 because 7.5… rounds to 8 since it’s based on only the next digit. That way you know numbers barely closer to 8 than 7-7.51, 7.58, 7.5006, etc.-round to 8 without checking any digit beyond the 5. For the same reason -7.5 rounds to -8 so that you know -7.53, -7.50009, etc. round to -8 just by checking up to the 5 in -7.5…
The answer is -7 as we should always round up to the next greatest no. Which is available If we have -0.5 as an example 0 will be the answer. Likewise for every negative number the lesser -ve value is the greatest.
Edit:but do checkout the question because it is written whole number in the bracket which seems to not be in the ground of the question as whole numbers do not contain -ve integers.
But according to chatgpt it says the -ve numbers should be rounded away from 0. So I was wrong.
The answer is -8.
I read phd level maths article for this question and still the answer is -8..yay!!
I learnt something new today🎉😂
SHE’S TAKEN AT LEAST 2 LINEAR ALGEBRA COURSES AND A LEVELS LINEAR ALGEBRA AND IS STILL HARDCORE CONFUSED ABOUT WHAT IT MEANS FOR A SPACETIME VECTOR TO BE TIMELIKE
That’s probably what floor and ceiling notation is for when rounding
actually i usually repeatedly watch your all videos i love your oxford university journey i miss all of your old videos 😢(take love from Bangladesh lucy dear)
it would be to -8 because of situations when we don't know the digits afterwards. For example -7.5 and -7.50001 round to the same whole number, but we know that -7.50001 is closer to -8. This is also the reason why we round 7.5 to 8.
When rounding, you use the greatest absolute value
As my math teacher always says, even if you don’t know or understand a math problem, just follows the rules and you’ll probably be correct
As a high school student using [-7.5] or finding it's greatest integer function would be done like -8+0.5 where the whole number part is GI i.e.-8, and {-7.5} would be .5
Hence -8 is your answer
It's wrong to say that when it's half way you always round up. Actually there's a concept called significant figures and in that there are even more detailed rules to round numbers and according to it, if the digit preceding 5 is odd, then you round it up BUT if the number preceding 5 is even then you leave it as it is.
Eg- 3.5------> 4
4.5------->4
So by that logic, -7.5 should be rounded off to -8
Hope this helps
I believe The general rule of thumb is anything from 0.49(not getting too technical) is rounded down, anything from exactly 0.5 is rounded up.
So 1.5 rounded to the nearest integer, would be 2.
1.4 would be 1.
I see where everyone is coming from, but I believe it should be -7 in order to conserve important properties of the round function, in particular 「round(x+n) = round(x) + n (where n is an integer)」
by that logic -7.9 would round to -7
I was gunna say -7 because it’s greater but someone mentioned where would you round -7.4, which would be to -7, so -7.5 would round to -8
It’s easy,-8 bcuz every time the number ur rounding off to is 5 or greater the number gets rounded off up
But -8 is smaller than -7 since it is negative value so -7 would be the answer
@@darksouls9279 yes ur correct but for rounding off I don’t think that rule applies u can check on google I’m correct ❤️
Whole numbers are positive integers including 0. Therefore, the nearest integer (*whole number*) to -7.5 is 0
Yes and no, I think the question is slightly wrong as whole numbers and integers are different, whole numbers cannot be negative but integers can
Hi Lucy! What college did you study at in Oxford? Do you enjoy it there? Love your videos btw ❤❤
To find it you can use [-7.5] (read as box -7.5) and its greatest integer function (GIF) will be -8
Bruh it's GIF is 7
@@onlytostudy2300 no, it will be -8.
I think you can just disregard the negetive as rounding was made for only possitive numbers and round it up to 8
7.6 is closer to 8, 7.5 is closer to 8
-7.6 is closer to -8, so -7.5 would be closer to 8
Hence youd round -7.5 to -8
If you were to round up a two-digit number in this case, the decimal range would be [-6.50; -7.49] to round up to -7, putting 100 numbers inside. Beyond -7.5, this would be -8
Do you have any tips and tricks to make linear algebra easier?
Linear algebra is already easy
The reason you round up is because when you reach the halfway point between the two numbers, you consider the second to be the nearest. You’re not rounding up on a positive scale, but rather increasing the absolute value, do it would be -8
There are different systems of rounding. In Java and JavaScript, rounding the number would give -7. I personally think it’s -8. It’s something to think about when dealing with these different systems. The programming languages add 1/2 then take the floor (rounds downs) which means it takes the nearest greatest number.
Ut just gets -8 according to GIF function
The rule is to round up for and after .5
So -7.5 gets rounded up to -7
So -7.9 would round to -7?
That doesn’t make sense. Just think of it in absolute terms. What would you do if it was positive? Round it to 8. In order to maintain the equality on the opposite side of 0, it’d have to round to -8
Think about it like a hole. If you dig "7.5" out of the ground and put it in a pile, that is a measurable amount. There is equally as much removed (negative) from the ground as there is added (positive) to the pile. And if you round 7.5 up to 8, if you make your pile bigger, in order to maintain the equality between the dirt removed from the ground and the amount in the pile, the hole becomes larger, thus more negative, therefore -7.5 rounds to -8.
Plz pin this bc I like my math explanations...👀
Disagree but do like your explanation 😊
-8 is its GIF
AND -7 is its LIF
its not about less or more its about how close and .5 is closer to one than 0
It’s the same distance
1-0.5 = 0.5
.5-0 = 0.5
Totally just sent this to my math genius friend …. Waiting for answer 😂
-8 makes the most sense to me since I perceive the xy plane directionally. So x = 0 is like a mirror and negative integers and positive integers move way from each other.
I don’t imagine the x plane as a continuous left to right progression of numbers (even though it is), it just made a lot more sense to me for everything negative to be right to left.
-8 just round with the scalar quantity (aka the value without the direction) then add the direction after
As an engineer, I would say it depends on what your worst-case is.
You would still round up, so -8. The thinking is -7.5 can be -7.50 to -7.54. Which you already know would round up to 8.
i like to think that, as 5 rounds to the furthest extremity to the right (i.e. it is closer to 10 than 0), as -7.5, -7.6, -7.7 and so on, means that -7.5 would round to -8
i think this calls into question the definition of the rule: what is meant by “greatest number”? the largest quantitative value (+ > -) or the larger number on a scale of 0.0 to 1.0
the former interpretation would lead to A, but the latter would lead to B
this is interesting!
Think about what's greater
Ex. 7.5 ~ 8 because here 8 is greater
While
Ex. -7.5 ~ -7 because here -7 is greater than -8
Hope this helped 😊
Hi Lucy!!! Love your videos! How did you choose to go to Christ Church college? What’s good/bad about it? ❤❤❤
It says (whole number). Whole numbers start from 0. Negative integers aren't whole numbers. So neither -7 not -8, it's 0!
I'm literally so happy 😂🎉
Whole number is an explanation for the integer. Not a part of the problem, that's why it's in parenthesis.
Natural numbers start from 0
@@tinkvaternjak9311 and who mentioned natural number here? It's an integer. Integers work with modulus, regardless of the sign before it. It's still an integer.
@@saharaliake8970Integers are not the same as whole number, so the question is either wrong or the answer should be zero. Since both the options do not represent a whole number
@@mayureshchaudhary8238 yeah but the statement of whole number is in brackets so the priority is the word integers not whole numbers. You should process integers. That's subsidiary info.
For example, let's consider the number -2.2. If we need to round this number, we compare it to the value -2.5. Since -2.2 is greater than -2.5, it rounds up and the result is -2. On the other hand, if we have -2.7 and need to round it, we compare it to -2.5.
G I F ( greatest integer function)
I would go with the larger version cause room for error is better.
Some science disciplines say that when rounding a 5 you round not up but to the nearest even number to avoid a slight upwards skew. In this case, i would round to -8 because it is the nearest even integer. If choosing not to use this rule with the rest of your rounding however, i would round up to -7
As an engineer we were told that we round so that its an even number, so it would be -8
Equat to - x . Multiple both sides to -. Round of and multiple - ansv-7
The two most common ways to round are to round ties away from zero or to round ties up (towards pos. inf). ...So it's either -7 or -8, your choice, or somebody else's but it's a choice.
I think this video shows that if u have such a rounding problem, best to not round at all 😂
Depends on the situation. If it’s half a cent of debt to a bank, they would definitely round to more debt.
Some might think of -7.5 as just 0 - 7.5, in which case you would round to 8, but if you treat a negative number as a value itself, you might round to -7.
I would round to -8 because I believe that a negative number is just subracting a positive (two reasons, 1: i can’t imagine an inherently negative value, 2: negative and positive numbers are treated differently [-7x-7=49, 7x7=49])
-8 is the only answer that is consistent. Imagine you had a set of equations that included negative signs (enthalpy perhaps).
For example x = -7.5 y =-x. Then y = 7.5. Say you round x to the nearest integer by going up, you get -7. Now say instead you rounded y by that method you get 8. Now y=-x and you have an inconsistency.
This is solved by rounding -7.5 to -8. This should be obvious to anyone who uses mathematics on a regular basis.
I basically see as moving away from 0. So 0.5 whether positive or negative or negative would move away from 0. While 0.4 whether positive or negative would move towards 0.
I think it should be rounded to negative three
-8 cause whenever it is .5 we round it up for nearest even number
In programming, the language Python rounds to the nearest even number (which seems like a very strange system) while Java adds 0.5 and then runs floor()
Python’s approach seems crazy, so I’ll go with the Java approach of always rounding 0.5 to the larger (more positive) number.
Bro you need to sleep sometimes, your eyes.
Judging from the question; the number -7.5 rounded to the *nearest* integer is -8, but if rounded to the *greatest* integer then it is -7.
-7 because when it comes units and measurements in physics, in our book their is a rule for rounding off digits, that if the number after digit is 5 then the number before is remained unchanged
i think if negatives as -1(n) so in that case i’d be -8
I see negative numbers like the flipped version,so if it's 8 in the positive form then i would see it as -8
My high school science class would say to round to the even number. In situations like this, when math fails, science prevails.
i think -8, because if you extend that decision to all negative numbers, when you have -0.5 your choices are 0 and -1. zero has several properties that make it hard to work with, so it makes more sense to round it to one. (i know one has it's own issues but at least you can divide with it and multiply without eliminating everything.)
-8
.5 rounds up, and since it’s negative it rounds down. Positive and negative numbers are like mirror images.
The rule i learnt was that if the preceding no was even then the no is reduced and if its odd then its increased
I would say -8 because you round up to the number that would have the greatest “effect”. We do this because it is usually better to overestimate something than underestimate it
The answer: it depends on context. In a data science context, rounding up away from zero (so -8) has a nice impact because on average the rounding cancels out, assuming the distribution is fairly distributed. Granted, in a language like Python, this isn’t the case, and rounding up always goes toward positive infinity. Why? Because that’s how the programmers wrote it, and it works well enough that people will just find a different solution if it doesn’t work in their context.
Mathematics is about discovering a lot of fantastic things, using human defined tools. The human defined part is important here, so really it doesn’t matter which way you go, as long as you’re following a clear convention
I think I have the right answer! If it's a vector then you should round it to -8 because the negative sign only indicates direction. It doesn't indicate any special properties about the unit so if you ever converted it into its absolute value, you would round it from 7.5 to 8.
If it's a scalar then it just depends on the context. For example temperature has negative values but if you're working with degrees in celsius then you have to remember that -7.5 degrees in celsius is going to be a positive number in Kelvin and I don't even want to talk about Fahrenheit. The easy solution is to just convert everything to Kelvin then do the maths that way unless for some reason it's super important to measure things with respect to freezing or boiling temperatures of water. Then celsius might be more appropriate and I think in that case they should be treated as vectors and rounded as absolute values.
There are other cases such as with distance or voltage where a positive or negative value is purely based on the starting point/point of reference. Is completely arbitrary.
At the end of the day, if you ever have to resort to rounding then you're not really doing theoretical maths anymore. You're probably doing engineering and in that case, the correct answer is to trial and error both options and go with whatever one works the best. Although it's probably not important anyway.
I use the rounding system my chemistry professor taught me, basically round to the nearest even number… so we’re not always consistently rounding up, making things greater than they should be
I’m gonna ask my maths teacher this
Can you please try solving GATE math questions?
GATE is an entrance exam for engineering students wishing to pursue a Masters degree in IITs
Its the greatest integer function. We look at the magnitide. Hence, -8
Except that’s only one of six commonly-accepted deterministic ways of rounding, especially when the fractional component is exactly 1/2. There’s nothing strictly forcing you to use the GIF, as you could opt for:
- Using the LIF (LIF(x) = n, where n - 1
@@matchamitminze now that is some mind blowing cool stuff 😌😌
I mean… rounding is subjective to the situation.
As an exact middle ground (7.5) you could go either to 8 or to 7 depending on what the situation is. If you assume rounding up for positive numbers (away from 0) you should do the same for negative numbers - go away from 0.
it’s -8 so that it is balanced
-7.0,-7.1,-7.2,-7.3,-7.4 -> -7
-7.5,-7.6,-7.7,-7,8,-7.9 -> -8
If u round -7.5 to -7, it means there’s almost always biased towards -7 when rounding from somewhere between -7 and -8 when it should be exactly balanced if it’s random.
The only time it doesn’t matter is when they’re real numbers and then (-7.5,-7] and [-7.5,-7] have the same size as the other half. But real numbers don’t exist in reality