density units

[mollykins]

while looking at a maths revisioni looked at reaaranging formulas, but there was something that confused me.

I know the density is mass / volume, but i've always done it as g/cm cubed, or another sensible unit like kg/m cubed. But in the book, it said g/cm to the minus cube, why? and what difference does it make?

[bibblebub]

x^(-3) = 1/(x^3) so it should be g cm^(-3) - no division sign needed

[mollykins]

well it means the same thing, grams per cubic centimetre.

[R1Geezer]

the minus cube mean a cube root so it must be in relation to some rearangement of he formula, can you post the whole statement.

[vascop]

No R1Geezer, x^(-3) does NOT mean cube root of x, it means 1/x^3. The cube root of x is written x^(1/3).
Bibblebub is right.
Another example would be:
speed =distance/time =s/t or s times t^(-1).
Using just numbers you can write things like:
2/3=2 times 3^(-1)=2 x 3^(-1)
1/2=1 x 2^(-1)=2^(-1) etc

[mollykins]

i can't do all the symbols so you'll have to bare with me. . . .

this is the example from the book . . .

calaculate the density of a rock of mass 780g and volume 84 cm cubed, give your answer to a suitable degree of accuracy.

density = 780/84 = 9.28571 g cm to the minus cubed = 9 g cm to the minus cube

with no explanation with the explanation or anywhere else on the page.

[vascop]

Yes, OK.
gram cm to the minus cubed is g cm^(-3) or gm/cm^3, which, because of what I said in my first post and so did bibblebub, is grams per cm cubed, the usual units for density.

[vascop]

Oh yes and ending up with 9 is just rounding to the nearest g per cm cubed

[vascop]

And that rounding is appropriate because you started off with a whole number of grams (780) and a whole number of cubic centimetres (84) and so quoting the answer to five decimal places or whatever doesn't make sense.

[vascop]

Strictly speaking it's incorrect to use that last '=' sign.

[vascop]

The reason this works is because of the rule that when you multiply the same quantity to different powers you add the powers:
x^a times x^b = x^(a+b), so:
x^3 times x^(-3) = x(3+-3)=x^(3-3)=x^(0)= 1
So x^(3) times x^(-3)=1
and therefore x^(3)=1/x^(-3) and vice versa.

[mollykins]

what have the rules of indice multiplication/division got to do with this?

[mollykins]

oh i think i get it, and thats the reason why the answer is to the minus 3.

[vascop]

Yes, You can either write:
g/cm^(3) OR
g cm^(-3) WITHOUT the '/' sign

[mollykins]

if we'd have had a proper maths teacher we'd probably learnt little tthings like that, but they concentrate on the big things that get you the most points, but if you want to get full marks and thus an a* you have to know the little details like that.

[beso]

Ideally they would be using the international scientific (SI) unit for density which is kg/m^3 (or kg m^-3 if you prefer). SI is an mks (metre kilogram second) system.

Grams per cubic cm is the obsolete cgs (centimetre gram second) system unit.

But then it is a maths question not science.

[R1Geezer]

sorry vascop, you are correct, confused the terminology.

[factor-fiction]

yes, g/cm³ is the same as gcm¯³