Incorrect work of members doesn't help students, not ...

[lookagain]

others pointing out how wrong the member's work presented to the student.

Ex. The following wrong work is shown by a forum member:

$\displaystyle \ \ \dfrac{1}{4} \cdot 100 \ = \ 0.25 \cdot 100 \ = \ 25\%$

Another forum member posts a correction so that the student/OP does not
learn the wrong way:

$\displaystyle \ \ \ \dfrac{1}{4} \cdot 100\% \ = \ 0.25 \cdot 100\% \ = \ 25\%$

When the post of the correction is removed, the member is rewarded for their
wrong work, and the student/OP goes away with more ignorance.

 

[Cubist]

Maybe this is a difference in preferred notation between the US and the UK. What are the experiences of other helpers?

I'm pretty sure that I've been taught (in England) to use % in a similar way to dimensions(units) like cm, °C, $ and so on. We'd usually state this in words at the start, for example:-

The flow, expressed as a percentage of the maximum flow, is f*100/f_max
OR Let p be the percentage increase in...

If the final line is numeric then the % symbol must also be shown at that point - but not everywhere between.

 

[Steven G]

@Cubist
My problem is that 100% does not equal 100.
How can it be that sometimes .25*100 = 25, while other times .25*100 = 25%.
I know that you are probably going to say that it is understood in the context.
I think that equal signs should have meaning and replacing 100 with 100% is unacceptable.
I try real hard to understand the culture that comes from other countries but sometimes I feel their culture is wrong.
In Kenya for example, school is in English while their national language is Swahili. I believe that they should pick one language for school and that same language for their national language. I know many Kenyans and they agree with me.
I am sorry but

 

[topsquark]

I have a similar issue with students (and sometimes professionals) who don't include units in their answers. It's not a good habit to develop and I often mention it, but sometimes you just have to live with it.

No offense meant to anyone.

-Dan

 

[Steven G]

I agree that we have to live with seeing no units. I too many times do not include units. I just really don't approve of going from 100 to 100%. You want to introduce %, so write 100% instead of 100.

 

[Cubist]

Interesting. It's good to know how others do things. Thanks for replying! I'll try to fit in. When on a Roman website... ?

 

[Deleted member 4993]

he member is rewarded for their wrong work

How does that "rewarding" work? I have made many mistakes - never been rewarded. Who is in charge of those rewards?

 

[BigBeachBanana]

How does that "rewarding" work? I have made many mistakes - never been rewarded. Who is in charge of those rewards?

You get to be close to your favourite people in the corner. That's your reward. I believe Steven is currently in charge or he's just there a lot. I'm not sure.

¯\_(ツ)_/¯​

 

[Steven G]

I believe Steven is currently in charge or he's just there a lot. I'm not sure.

¯\_(ツ)_/¯​

Both, but currently out on parole.

 

[lookagain]

I agree that we have to live with seeing no units. I too many times do not include units. I just really don't approve of going from 100 to 100%. You want to introduce %, so write 100% instead of 100.

The percent symbol is not even a unit. It has no dimensions. It means to divide by 100 or
multiply by 0.01.

 

[Cubist]

The percent symbol is not even a unit. It has no dimensions. It means to divide by 100 or
multiply by 0.01.

I guess that "specifier" would have been a better word than "unit"? The percent symbol specifies something about the associated number.

I just had my mind blown by this page about dimensionless quantity. Some consider the (angle measure) radian to be dimensionless. Also the measure of speed "mach" is a ratio between the speed of an object to the speed of sound in the same medium, therefore it has no dimensions That's too much thinking. It's time for a big mach

 

[BigBeachBanana]

Some consider the (angle measure) radian to be dimensionless

I'd say that the unit is dimensionless if it has the same magnitudes in different units. Radian is the ratio of the arc length to its radius length, where the unit of lengths cancels out.
$$1 \text{ rad}=\frac{1km}{1km}=\frac{1mm}{1mm}$$In other words, it doesn't matter if you drew your circle with a radius of 1km or 1mm, 1 rad is still 1 rad. This is the advantage of dimensionless units, we no longer need to know what system the unit was used.
However, lengths themselves are not dimesionless for an obvious reason: $1km=1,000,000mm$ and $1\neq 1,000,000$.

 

[Cubist]

I'd say that the unit is dimensionless if it has the same magnitudes in different units. Radian is the ratio of the arc length to its radius length, where the unit of lengths cancels out.
$$1 \text{ rad}=\frac{1km}{1km}=\frac{1mm}{1mm}$$In other words, it doesn't matter if you drew your circle with a radius of 1km or 1mm, 1 rad is still 1 rad. This is the advantage of dimensionless units, we no longer need to know what system the unit was used.

Nice!

However, lengths themselves are not dimesionless for an obvious reason: $1km=1,000,000mm$ and $1\neq 1,000,000$.

I did an internet search and apparently there's a unit milliradian, abbreviated with the SI symbol mrad (click). I've never heard of this before, but it seems obvious. Therefore the above quoted reason also applies to quantities without dimension?

There's also a centiradian, and dare I say it, that seems quite similar to a percent of a radian

 

[BigBeachBanana]

Therefore the above quoted reason also applies to quantities without dimension?

Maybe that's not the best argument because you can always come up with arbitrary conversions like degree. i.e. $1\,rad=\frac{180\degree}{\pi}$. Obviously if we ignore the units $1\neq \frac{180}{\pi}$, but radian still dimensionless.
I probably should've stuck with the definition: "dimensionless unit is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one."
Since radian is dimensionless with a SI unit measure of one, milliradian is just an arbitrary conversion $1\, rad = 1000\, mrad$. There's nothing stopping me from defining something like $1\, rad=0.3\, \text{Cubist}$, but it's an obvious choice to go with base 10 since it's easy to work with (a reason to obliterate all of the English metrics), but again it's still dimensionless.
I hope what I'm trying to say makes some sense. This is beyond my expertise, but it was amusing to think about.

 

[Cubist]

I hope what I'm trying to say makes some sense. This is beyond my expertise, but it was amusing to think about.

Yes it makes a lot of sense, thanks. I think having used a rule and protractor together I had just associated both of them with measuring something physical - with having a dimension - and I was wrong!

In a strange coincidence, I read the following in the news today, "an angle on the sky that is measured in microarcseconds". This was regarding the black hole image released today of Sagittarius A* at the centre of the Milky Way. Here's a link to the news article. However, I wish they'd given the angle in femtocubists

I'm not completely sure if this is related to the dimensionless/ ratios discussion, but last weekend I had a very old instrument in my hands called a sector (click). It performs calculations using ratios (angles?) but I don't know how it worked, I haven't read up on it... yet

 

[The Highlander]

Yes it makes a lot of sense, thanks. I think having used a rule and protractor together I had just associated both of them with measuring something physical - with having a dimension - and I was wrong!

(Just noticed this comment of yours.)
You were not "wrong" at all!
The things you were measuring with your rule and your protractor (I can just picture you behind your desk: school cap, short trousers, dirty knees and socks at half-mast; protractor in one hand and rule in the other) did have dimensions, you just occasionally use a measure (eg: rads) that has no UNIT ie: is a pure number (why it's so handy in Maths!)
Any RATIO is dimensionless; cf the trigonometric ones, they are all pure numbers, innit?

 

[JeffM]

The measure of this angle is 1.

One what?

I get the argument that a ratio of two lengths does not have any units involving length, but we still need to specify the unit being used to measure angles. Is it degrees, grads, or radians, a unit in other words.

I think the real point about radians arises when we start using trig functions outside the domain of trigonometry and geometry and use them to describe periodic functions generally. At that point, the arguments of trig functions have no relation to geometric figures, and using radians simplifies calculus. They, like natural logs, just are super-convenient in calculus.