Quite often I write my expressions like the ones below:
I write it as: 1000N * 3m = 3kNm
is this incorrect as I haven't written the *10^-3?, that is;
1000N* 3m *10^-3 = 3kNm
or another example with percentages:
I write it as: (5-4)/4 = 25%
is this incorrect as I haven't written *100%?, that is;
(5-4)/4 *100% = 25%
The first one is confusing me. where did 10^-3 come from?
1000N*3m = 3000Nm (3kNm which is your notation but personally I don't like it much.)
10^-3 = 0.001 it is not 1000
10N* 3m *10^-3 = 30Nm/1000 = 0.03Nm NOT 3000Nm and not 3kNm
The second one is fine.
1/4 is the same as 25%
No, I think you have made it worse. it is the minus index that is wrong.
1000N* 3m *10^-3 =3000Nm/1000 = 3Nm NOT 3kNm
interesting. I see how you're getting confused.
This is how my teaching team have been writing their expressions over the years the
*10^-3 is meant to signify the coversion from 3000N to 3kN. It's not suppose to be a part of the mathmatical problem.
I hope that makes sence
To relate to the percentage example above,
I guess it could be written as "*10^-3kN"
"This is how my teaching team have been writing their expressions over the years "
Your teaching team needs to be shot!!!
You don't say what the units of 281.25 are. Presumably they are kN.m. (Edited again!)
This means that 281.25 kN.m = 281.25*106 N.mm or it could be written as 281.25*103 N.m
In terms of your original question you could have: 1000N*3m = 3000N.m or 3*103 N.m or 3 kN.m but you should never see 10-3 appear anywhere here!
"interesting. I see how you're getting confused.
I hope that makes sense"
You may find it 'interesting' but I do not think it is me who is confused.
And no, what you have written does not make sense.
I can see exactly where you're coming from. I believe that this issue so systemic throughout my facilty that most (including myself until now) do not know we're writing it incorrectly. I can see your way as correct.
I guess we've essentially made our own language while being oblivious to it.