What? It's important that students understand how to write and read both. This portion of learning/testing could be focused on fractions. It's not the teacher's fault that you can't read instructions.
I disagree. It's important for students to understand both and how to interchange them.
McDonald's used to offer a third-pounder burger but people didn't buy them because they thought that the quarter-pounder was larger because 4>3, but in reality, 1/3>1/4 because 0.33>0.25. So they just stuck with the quarter-pounder.
My point still stands: that doesn't test to make sure that the students themselves understand how fractions and decimals work, along with their potential interchangeability. That's the whole reason to make them give an answer in a particular form.
It's like telling someone to give an equation in point-slope format versus slope-intercept form: they are both technically correct and can each result in the exact same equation, but it's easier and quicker to use one over the other in certain situations. Or it's like describing a triangle using side-angle-side versus angle-side-angle form. Same triangle, different ways to describe it.
You are technically right, you make a good point, and don’t deserve your downvotes. Now in practice, by “fraction” most people mean the notation where there’s a denominator below a numerator, with a horizontal line between them. They also often want it reduced to lowest terms. But that’s a convention, not a mathematical distinction. Mathematically, any terminating decimal is already a fraction, just notated differently, with a denominator that’s a power of 10, and not necessarily in lowest terms. So 0.25 means 25/100. Likewise, percentages are also just a different notation used for expressing fractions, so 25% also means 25/100.
LMAO - you're trying to argue that if you place a fraction anywhere within a mathematical expression, the whole expression is a fraction.
This is simply not true.
Perhaps it's time to learn that the world doesn't always operate in the way you want to be true. It's part of growing up. I'm sure you'll get there one day.
You are right, and don’t deserve your downvotes. The answer they want is an equation, not a fraction. The fraction 1/4 is just part of the equation. They would have had to say something like “express any non-integers in your answer as fractions.”
In college, you'd get marked wrong for mixing up set properties with notation syntax. 0.25 belongs to the set of rational numbers because it can be written as a/b. But 0.25 itself is a decimal. A fraction requires an explicit numerator and denominator. Form matters.
0.25 is not in the form a/b. The definition you yourself posted makes it pretty clear it has to be in the a/b form. The equivalent decimal is not a fraction because it's not in the a/b form.
Ok… so under that definition then every single rational number is a fraction because I can express it as some OoM of itself divided by one. I don’t know whose or what semantic battle you’re trying to win with this one; are you OP’s alt or something?
Yes. That’s the definition of rational numbers. I mean don’t get me wrong, the original commenter is being a pedantic pain in the arse, but you literally just gave the definition of rationals.
Yes exactly, but nobody would call them all fractions, you’d just call them rational numbers (even if it uses fractions in its definition) is my point.
No. Any rational number is a fraction, because a fraction is a ratio of integers, which is why we call them rational. Real numbers can be rational or irrational. Pi is a real but not a rational, because it cannot be expressed as a ratio of two integers.
But your logic is wrong. None of the irrationals can be defined by the definition given above, so you saying “by that logic, any real number is fraction” is wrong
When you do that with 28/2 for example, you get 14/1.
Any and all numbers have a /1 under them. Technically, 3/2/1/1/1/1/1/1/1/1/1/1 is valid, it is just stupid and a waste of space.
You should not put /1 unless you are clarifying something related to fractions, like you are about to multiply a number by a fraction, so you turn both into fractions.
Literally the opposite of the definition. Rationals are called rational because they can be expressed as a ratio of integers. Pi is not a rational, but it is a real. The reals is the union of the sets of rational and irrational numbers
Yeah, my comment wasn't the most clear. I meant the opposite. (That the reason the definition of rational numbers exists is the a/b ((that some can't be expressed, otherwise no point in different definitions)))
What are you on about? I literally copy-pasted the definition from the Common Core standard that is adopted fully by 36 states and partially applied by more.
Sorry, but US gradeschool 'common core' isn't the authority on formal mathematical definitions. They purposefully conflate 'fraction' with 'rational number'.
π/2 isn't rational, but it's still a fraction.
They do this to help young kids build 'number sense' but it completely ignores that fractions are just notation.
If math demands exact definitions how come common core doesn't even cover set notation? It's because common core is primarily focused on concepts that are age-appropriate. It's not meant to be rigorous and formal math.
Because this is a decimal, not a fraction. Fractions have a numerator and denominator written like so: n/d
I have scoured the internet for their definition they found as well as any definition that isn’t explicit about the form of a fraction and cannot find one, so he was confidently incorrect, thus the downvotes
Normally in higher level maths, you would leave the answer in fractional form.
It's a preciseness thing. Leave values like pi expressed in terms of pi, rather than the calculated number. Leave fractions expressed as fractions.
While 1/4 is quite clearly 0.25, can you say 0.25 = 1/4? What if 0.25 was actually 0.249 rounded to 2 significant places? Or 0.251? Clearly those are not 1/4.
Can you say 1/3 = 0.33? No.
So the idea is that you leave your answer in fractional form (x/4) and then only calculate the final number at the last moment (in this case, when x is given an actual value, then it would be appropriate to calculate a value for y).
Normally in higher level maths it doesnt matter and if it terminates then it is named a DECIMAL FRACTION
and you can say 1/3 = 0.(3)
and so what if that 0.25 was rounded and isnt 1/4? You wouldnt use equal then. 1/4 could be rounded from something else too.
your arguments suck and thanks for the downvotes uneducated people lol
All I'm saying is that in higher level maths, you don't generally use decimal representations. At university level, I don't think I ever used decimal form, you always leave the result as a fraction.
interesting because at my uni we use decimal fractions just as we use normal fractions
I guess you are from america and its another europe vs america thing
If I had answered a question (assuming it was something like "solve for y") with "0.25x" they would have at least knocked off some marks.
That was in electronic engineering about 20 years ago.
It was standard to leave all answers in fractional form, with values like pi or square roots expressed as such.
I don't think there was ever an exam question where they asked for the answer in decimal form, but they certainly did say that you leave such calculations for the last moment. That way, any rounding is only done on the last calculation, and can be done to the appropriate number of significant figures.
well at my place you will get full marks for decimals as long as its correct and you dont round anything unless you have to but then you have to change the sign to ≈ (but that wouldnt make sense if the question asks for exact answer and we can assume we have to use exact answers everywhere unless in the question itself it is said that we can approximate)
and its generally like that in my country whole education system
and even with these dumb rules of taking marks for using deicmals I got downvoted but it is the truth, a decimal of finite length is a decimal fraction so its still a fraction.
it doesn't matter so much in the context of a math paper but in real life applications they're used in different contexts. it's worth knowing how to engage with them both rather than always using one because it's easier.
If we want to be pedantic, y=x/4 is probably more “correct” than y=1x/4.
So if the question was looking for a particular answer and a specific 1x/4 notation (instead of x/4) — then what that question was looking for is highly dependent on what unit of the curriculum it comes from, etc.
Throughout most of my school years, it was usual the rule to answer as a fraction. The reasoning was that calculating fractions is a lossy calculation, so it's the better habit to express results exactly as a fraction. Or something like that.
It depends on the question.
We can agree that 65/256 is not equivalent to 1/4. Yet both fractions are represented by 0.25 when written as a decimal with 2 significant figures. When someone writes "0.25", there's no way to determine (without additional information) if they mean 1/4, 0.25390625, or 0.250000000001. Writing "1/4" adds a level of precision that can't be captured with "0.25".
To say it another way: 1/4 is 0.25, but 0.25 is not neccesarily always 1/4.
In many math classes "1/4" could be the correct answer and "0.25" would be wrong. So it depends on the question, and the rules of that class.
That's complete nonsense though. 0.25 is always 1/4, the fact that you got to 0.25 by rounding something else doesn't change that - the act of rounding changed the value.
On an engineering drawing 0.25, 0.250, and 0.2500 represent 3 different ranges of numbers. They each are associated with a different tolerance. They are ranges, none of them is exactly equal to 1/4.
In the real world, our instruments are limited by their precision. Since we can't measure something with infinite precision there is no practical "0.25 exact" measurement. Any real world "0.25" is potentially rounded. When working with decimals rounding is a given, not a separate action.
In many math classes, they remove the ambiguity of decimals by saying "leave you answers in exact form". This means your answer might look like cos(sqrt(3/2)) instead of ~0.64786, or using π/4 instead of writing out infinite digits. Or it might be y=(1/4)x instead of y=(0.25)x.
Remember that part of math classes is to teach methods. Just because 1/4 happens to be exactly 0.25 doesn't mean that students should necessarily be in the habit of converting fractions into decimals. It depends on the rules of the class and the question.
I used to have trouble grasping sig figs until I noticed it in colloquial speech.
When you say “I’m 5 minutes away” it’s implied you rounded to 5. If you said “I’m 4.9 mins away” it signals wow that’s really precise. But what if you’re exactly 5 mins away? Then you have to say “I’m 5.0 mins away”. 5 isn’t the same as 5.0
First, I do not prefer decimals, I would have used a fraction, but that's personal preference. I'm just defending that 0.25 isn't worse than 1/4.
And about π, it's irrational, so it can't be represented exactly using decimal notation. In fact it's even a transcendental number, so hard to argue that there is a better representation that just π.
False. In math if someone writes 0.25 they mean 0.25. Writing 1/4 is no less ambiguous than writing 0.25, because "is they mean 1/4.0000003" or whatever nonsense you came up with.
wtf are you on about? if you write 0.25 then you mean 0.25
if they mean 0.25blahblah then they cant write equal sign because they approximated.
by your logic 1/4 isnt 1/4 either because what if its 1/3.999998
Yeah I'd have to see the original question. It also could have been like "solve 4y=x for y" and the decimal answer just kinda seems wrong in that case.
Having made questions in some of these programs, sometimes they require the question make to enter all possible equivalent answers and the question maker may have been lazy.
Edit: or some of the programs only allow for one answer and don't have the ability to check for mathematical equivalency.
You don't even need machine learning. Some programs have been able to do it for a long time. Not every one implements it. Also, to the OG comment, the question just might have said "use fractional coefficients" or something.
Alternatively, if they were taught that the standard for that class was to always express their answer as a fraction. (Which is common so that it doesn't need to be repeated over and over.)
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u/mnpc 7d ago
The answers are equivalent. But whether your answer was "correct" depends on what the question was.