Ahh, fractions and word problems, the bane of my education (seriously, why do we bother with fractions when decimals are easier to compute and express?)
The higher the level of the course I was taking, the less test markers cared about the actual final answer. If you used the correct equations, simplifying the final answer to a faction rather than a decimal or leaving constants like pi and e in there was good enough for full marks.
Generally more accurate, too, because you’re not rounding the number but leaving it as the true value because 1/3 != 0.333333. It’s better to do it this way if there’s multiple steps, too, since you can gather or cancel out like terms if you leave them as variables instead of converting and rounding to some decimal.
The fraction 1/3 is a compact and unambiguous representation—it doesn’t rely on an ellipsis or an understanding of infinite series to be interpreted. It can easily be used in later calculations (you never see … notation in algebra). It is a useful notation.
As soon as you use decimals in computer and human calculations, they become lossy.
I’m not really sure what hill you are trying to die on. Fractions are useful, even if you don’t know how to use them.
well, no, it’s understood that a third is .333 to infinity, so .333+.333+.333 does equal 1 for any use not requiring precision to the point of it mattering that it was actually .33333335 when measured.
It came from it not being actually .333 to infinity when measured in the required engineering precision i was talking about. It’s literally a “common use” mathematical convention (you clearly are unaware of) that three times .333 is one. Solves a lot of problems due to a failure of the notation.
You knows when a person informs you of a convention people use to solve a problem created by notation, you could just fucking learn instead of arguing stupidity.
People have already commented on fractions, there’s a lot of math that is way easier to keep accurate by leaving in fractional form as it goes.
For word problems, done correctly, the math is pointless if you can’t map it to more realistic scenarios. In terms of applying math to the real world, it’s supremely rare that the world just spits out the equation ready for you to solve, the ability to distill a scenario described by prose to a mathemetical solution is critical. Problem is when they are handled incorrectly and have ambiguous solutions or parameters, but dealing with kids’ homework, this is pretty rare, though it’s admittedly utterly infuriating when it comes up.
Imo fractions are way more simple in many cases than decimal numbers. Saying 1/3rd is way more useful than hitting someone with the 0.33333333333333…
Quick mental computations with fractions are also simpler in this case. Though this question (and questions like it) seem useless to me indeed.
Possible, but at least in my experience most normal people know 1/3rd and understand what it means, but if I’d throw a “point three repeating” at them they’d probably get confused. Fractions are just a tool to communicate stuff more efficiently, good in some scenarios, confusing in others. It would be cool if we could teach everyone the “repeating” syntax as well because it’s another useful tool.
In many cases that’s fine, I’ve done so regularly. But when you want to be precise without making it complicated you can just say the fraction as well. But in order to do that you need people to feel comfortable with it, therefore we need to teach kids this from a young age. I’m not saying we always need them, but they’re definitely very useful tools that you want at the ready when you need them. To make quick calculations in your head it’s often way simpler to use the fraction than the real number. And in cases like 1/3rd or 3/7ths it’s a way simpler, accurate and more efficient way to communicate the number than to name the rounded number.
At least where I am from we do get fractions in school.
Most people here will say “een derde” aka a 3rd, but it is mostly not used as a precise measurement or anything.
Something like 3/7th is rarely used andd we would say 42,9%. In cases where the differences that create are relevant we would communicate it on paper or digitally where iirc we would still use percentages or decimals. Then again I am an accountant and not a technical analysist or anything. For me the difference between 42,9% and 42,85714 will mean a couple thousand at most.
Doesn’t imperial metrics also use frations from time to time? Metric doesn’t do that, but we have things like nanometers etc.
It’s not about accuracy especially not when TALKING to somebody. I work with numbers for a living and nobody is as obsessed with fractions than people on Reddit and Lemmy, it’s crazy and I have clients where the difference between 33,33% and 33% can be thousdands of euro’s.
Ahh, fractions and word problems, the bane of my education (seriously, why do we bother with fractions when decimals are easier to compute and express?)
The higher the level of the course I was taking, the less test markers cared about the actual final answer. If you used the correct equations, simplifying the final answer to a faction rather than a decimal or leaving constants like pi and e in there was good enough for full marks.
Generally more accurate, too, because you’re not rounding the number but leaving it as the true value because 1/3 != 0.333333. It’s better to do it this way if there’s multiple steps, too, since you can gather or cancel out like terms if you leave them as variables instead of converting and rounding to some decimal.
Man, if you can’t understand fractions, you don’t actually understand the math, you’re just trained to use a formula.
I understand fractions, I simply doubt their utility.
Hate to break it to you but anything less than a whole is a fraction of a whole thing. Decimals, too, are bits of a whole.
Saying shit like that implies you don’t really get that they are the same thing.
For example, they allow you to write
1/3 + 1/3 + 1/3 = 1
Which is not possible in decimal
Tf you mean?? You can write it in a repeating decimal as
0.333....using ellipsis. https://wiki.froth.zone/wiki/Repeating_decimalSo you think
0.333.... + 0.333.... + 0.333.... = 1Is clearer and more concise than
1/3 + 1/3 + 1/3 = 1
Fractional representation is the method for rational numbers, particularly if they are part of an intermediate calculation.
Decimals are lossy, fractions aren’t.
No because you said this:
You can also precisely write to infinity if you write 0.333…
Decimals aren’t lossy, any fraction can be converted to decimal but it just takes longer to write.
The fraction 1/3 is a compact and unambiguous representation—it doesn’t rely on an ellipsis or an understanding of infinite series to be interpreted. It can easily be used in later calculations (you never see … notation in algebra). It is a useful notation.
As soon as you use decimals in computer and human calculations, they become lossy.
I’m not really sure what hill you are trying to die on. Fractions are useful, even if you don’t know how to use them.
What does lossy mean? I’m not trying to die on any hill, but I’m quite confused aswell.
well, no, it’s understood that a third is .333 to infinity, so .333+.333+.333 does equal 1 for any use not requiring precision to the point of it mattering that it was actually .33333335 when measured.
No. You wrote .333
If you want to precisely write to infinity you write 1/3.
Holy fuck. Where did that 5 come from?
It came from it not being actually .333 to infinity when measured in the required engineering precision i was talking about. It’s literally a “common use” mathematical convention (you clearly are unaware of) that three times .333 is one. Solves a lot of problems due to a failure of the notation.
3 times 0.333 is 0.999 not 1.
Saying it equals 1 may be a common engineering convention, but it is mathematically incorrect.
There is no failure of notation if fractions are used, which is why I gave this example of usefulness.
You knows when a person informs you of a convention people use to solve a problem created by notation, you could just fucking learn instead of arguing stupidity.
People have already commented on fractions, there’s a lot of math that is way easier to keep accurate by leaving in fractional form as it goes.
For word problems, done correctly, the math is pointless if you can’t map it to more realistic scenarios. In terms of applying math to the real world, it’s supremely rare that the world just spits out the equation ready for you to solve, the ability to distill a scenario described by prose to a mathemetical solution is critical. Problem is when they are handled incorrectly and have ambiguous solutions or parameters, but dealing with kids’ homework, this is pretty rare, though it’s admittedly utterly infuriating when it comes up.
who says, 5/6 is easy to mentally understand than 0.83־.
is a reasonable way to start thinking about arithmetics, and basically to start doing simple math IMO.
Imo fractions are way more simple in many cases than decimal numbers. Saying 1/3rd is way more useful than hitting someone with the 0.33333333333333… Quick mental computations with fractions are also simpler in this case. Though this question (and questions like it) seem useless to me indeed.
I mean I understand, but in the case of .33333333333333… isnt it actually represented as “point three repeating”?
Possible, but at least in my experience most normal people know 1/3rd and understand what it means, but if I’d throw a “point three repeating” at them they’d probably get confused. Fractions are just a tool to communicate stuff more efficiently, good in some scenarios, confusing in others. It would be cool if we could teach everyone the “repeating” syntax as well because it’s another useful tool.
Or just say 33%?
In many cases that’s fine, I’ve done so regularly. But when you want to be precise without making it complicated you can just say the fraction as well. But in order to do that you need people to feel comfortable with it, therefore we need to teach kids this from a young age. I’m not saying we always need them, but they’re definitely very useful tools that you want at the ready when you need them. To make quick calculations in your head it’s often way simpler to use the fraction than the real number. And in cases like 1/3rd or 3/7ths it’s a way simpler, accurate and more efficient way to communicate the number than to name the rounded number.
At least where I am from we do get fractions in school.
Most people here will say “een derde” aka a 3rd, but it is mostly not used as a precise measurement or anything. Something like 3/7th is rarely used andd we would say 42,9%. In cases where the differences that create are relevant we would communicate it on paper or digitally where iirc we would still use percentages or decimals. Then again I am an accountant and not a technical analysist or anything. For me the difference between 42,9% and 42,85714 will mean a couple thousand at most.
Doesn’t imperial metrics also use frations from time to time? Metric doesn’t do that, but we have things like nanometers etc.
I’m also Dutch so I don’t have the answers about the imperial system haha
33.33333333333…%, you mean?
In 99/100 of the situations people do not care about you saying 33% instead of 1/3 or 33,3333333333% or 33,33…%
Shocking twist: boldly estimating 99/100 of situations is less accurate (more hyperbolic) than asserting 33% or ⅓ or whatever is accurate.
It’s not about accuracy especially not when TALKING to somebody. I work with numbers for a living and nobody is as obsessed with fractions than people on Reddit and Lemmy, it’s crazy and I have clients where the difference between 33,33% and 33% can be thousdands of euro’s.