# Right or wrong to put equality between two different units

• STAii
Oh 1n = 1 kg-m/s^2."In summary, a student was debating with his math teacher about whether it is right or wrong to put equality between two different units. While the student saw this as a valid practice, his teacher believed it was incorrect and suggested using the words "equivalent to" instead. The student's argument was that since both units are measuring length, it is acceptable to use the equal sign. However, the teacher argued that it could be confusing to use the equal sign in this context. Ultimately, it was left unresolved as both parties had different perspectives on the matter."

#### STAii

Well, i hate to put silly questions on the forums, but i had to do it this time !
Today i was arguing with my Math teacher on wether it is right or wrong to put equality between two different units.
For example, to say that :
1 Metre = 3.4 Foot (i am not sure of the number ... anyway !).

I personally see this is right, althought the two numbers are not the same, different units allow us to write equality between them, and from that we can derive that :

1=(3.4 Foot)/(1 Metre)

Which makes lot of sense when thinking why we multiply by 3.4 when converting metres to feet.
Since we are actually only multiplying by 1 (take the units in account), then it is right.

But my teacher sees that putting the equality sign is wrong.

What do u think ?

I think 1 metre =3.4 FEET is the correct from...(the plural)

STAii, I think it's a matter of personal taste.
Maybe it's not so good to mix words with math symbols. If you write
1 hour = 3600 seconds
that could be rearranged into
1 seconds = 1/3600 hour
See, you get problems with the plural.
I think it's better to state "1 hour has 3600 seconds" and then abbreviate to
1 h = 3600 s
which is an equation and may be rearranged any way you like.

1m= 3.??ft

1 = 3.??ft/m = 3.??'/m

I do not see the problem? Just learn to be lazy and use the abbreveations the plural is for grammer not math.

Staii, you are correct. the equality is perfectly valid. what s the deal with your math teacher? what does your teacher claim you should do instead of writing the equality 1 ft= 12 in? what level teacher is he? like high school, grade school? i assume it s not a college prof, a prof should know better...

The bottom line is that both 'foot' and 'meter' are units of LENGTH. The equation '1 meter = 3.28084 feet' is dimensionally consistent, because both the left and right hand sides are in units of length. This is the only criterion for an equation to be mathematically valid.

On the other hand '1 meter = 3.4 feet' is dimensionally correct, and mathematically valid, but is a false statement.

- Warren

Well, to make some points clear.
My question was not wether to write it "foot" or "feet" .

The teacher says we should say "1 meter is equilavent (sp?) to 3.2 feet" without using the equal sign anywhere ...

He is a 11th grade teacher (i think you call this Junior in the american system of education .. right ?).

We get into conflict of opinions almost twice each class (That is, twice a day), but i am glad that he always accepts other point of views and ideas ...

BTW chroot, thanks for the accurate value "equivalent"?
AFAIK, the equivalent relation (abbr.: <=>) applies only to statements. Let A and B be statements, then A <=> B means: A is true if and only if B is true.
On the other hand, the equal relation applies to values. Since 1 m and 3.28084 ft are values, the = sign is the correct one.
I think lethe's question points into the right direction. Does your teacher also teach lower classes? If yes, I suspect he does problems there like "One apple is 30 cents, how much is (are?) 3 apples?" The average kid writes down "1 apple = 30 ct" and then the teacher has to say "No, it's not equal, use another sign...!" and that may come out as 'equivalent', totally abused and wrong there... just an idea.

Well if you draw two lines on the floor, one of them 1 meter long and the one next to it 3.whatever feet long, then what can we say about the lengths of those two lines? They are EQUAL.

An expression like x {your favorite unit of length} stands for a length, and if two such expressions stand for the same length then they should be equal, meaning this length equals that length. I can see the teachers point about equivalence, but this kind of fussy fascism is enough to kill anybody's interest in the subject.

Reminds me of a Soviet-era physics test in Russia. Question, what is the pressure of a liquid in a container of a certain density and depth in the normal direction to the wall? Any numeric answer was marked wrong because pressure, not being a vector, can't have a normal or any other direction. Said to have been used to downgrade Jewish students by an antisemitic examiner.

you should definitely use an equivalence symbol; three horizontal lines.

Well, he doesn't teach any other grade than 11th (our school is so big that we have 3 math teachers ONLY for the 11th grade classes (which is made of about 600 student, the whole school is about 8000 students)).
BTW, Big schools are so bad !

jopnnylane, you don't agree on using the equal sign ? if so, why not ?

im not saying its wrong, but equality and equivalance are different things. To be honest, anyone would understand it if they saw it, and saying its wrong is pretty picky.

physicists get a fair amount of stick for using incorrect notation. Even in programming we get it, with our appently "rigid" code.

write it how you like; as long as people understand it, that's fine by me.

STAii, in 8th grade my math teacher told us there was a zero year. I bet him a soda there wasn't - he gave me the soda but never admitted he was wrong. Apply to your situation: you'll have to let it go because he's the one giving out the grades.

When you get later into your science classes you will use your exact reasoning to work out units in problems.

example:

f = m * a

f = 1kg * 9.8m/s^2

f = 9.8kg-m/s^2

Then apply the conversion: 1 = 1n / 9.8kg-m/s^2

f = 9.8kg-m/s^2 * (n / 9.8 kg-m/s^2)

f = 1n

When I learned unit conversions I leaned to think of it as multiplying by 1.

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Well jonnylane, i can mistype half of my reply, you can still understand it, but it woulnd't be right !
See my point ?

Russ_watters, I got what you mean.
For the last (some) years in school, i have been facing this kind of problems with math an physics teachers, they were almost never flexbile (i don't really care about the marks anyway !)