[Luke149]

Hi, im having a problem converting between two concentrations, the concentration im given is in g / 100 cm^3 and i need to convert this into kg / m^3.

My attempt at converting it so far is as follows. For the first concentration i have 0.4 g/100cm^3 which is equal to 0.004 g/cm^3, if you then multiply this by a 1000 you get 4 kg/m^3.

Ive always found it really had to get my head around conversions so if anyone can give a description of how you would do it i would be really appreciated.

Thank You

Luke

[Luke149]

OK i just realized i was being a bit of a fool since g/100cm^3 = g/m^3 so dividing by 1000 gives kg/m^3

[sjb]

OK i just realized i was being a bit of a fool since g/100cm^3 = g/m^3 so dividing by 1000 gives kg/m^3

Not quite. 100 cm³ is not 1 m³.

[Luke149]

Ok im really stuck with this ive spent hours trying to understand how to convert g/100cm^3 to kg/m^3 and im just not getting anywhere. Can anyone help my understand what to do? Many Thanks

[Borek]

Do it step by step using so called dimensional analysis.

Do you know how to cancel units?

Do you know that there are 1000g in 1 kg? In other words there is 1kg per 1000 g, so 1kg/1000g is our conversion factor, if you multiply

0.4 g/cm³ * 1 kg/1000g = 0.0004 kg/cm³

and that's the first correct step. Now convert cm³ to m³.

[Luke149]

Ah i think i understand so to convert 100cm^3 to m^3 you would do

1cm³ = 1x10^-6m³
100cm³ = 1x10^-4m³

So in 100cm³ there are 1x10^-4m³

Therefore

0.0004 kg/cm³ * 1m³ / 0.0001cm³ = 4 kg/m³

Is this correct? Thanks for the help it was much appreciated

[Luke149]

Ok so ive had a go at another conversion problem to check im understanding what to do. The problem is convert 0.4 g/100cm³ to g/dm³ my solution is:

1dm³ = 1000cm³ so there is 1dm³ per 1000cm³

but since the origional units are in g/100cm³ the conversion factor is 1/(1000/100) = 0.1

therefore 0.4g/100cm³ * 0.1 = 0.04g/dm³

Is this correct? Thank You

[Borek]

1cm³ = 1x10^-6m³
100cm³ = 1x10^-4m³

Correct.

So in 100cm³ there are 1x10^-4m³

Correct, but not necessary. It is enough to know what you write earlier, there is 1m³ per 1000000cm³, so

100 cm³ = 100 cm³  * 1m³ / (1000000 cm³)

What we are doing is we multiply initial volume by the conversion factor. Conversion factor is constructed in such a way that is in fact equal 1, so multiplication doesn't change anything when it comes to the value, however, it has units selected in such a way that cm³ cancels out and we are left with m³ only:

100 cm³ = 100 cm³  * 1m³ / (1000000 cm³) = 100/1000000 m³ = 10^-4 m³

1m³ / 0.0001cm³

See above, this conversion factor is incorrect. Plus, it goes in the wrong direction - check what units is your answer in (cancel units and check what is left).

but since the origional units are in g/100cm³

I would say original units are g/cm³, 100 was a volume. It is possible to proceed as you are proposing (that is assume 100 cm³ should be treated as entity) but it is easier and safer to not to.

[DrCMS]

Ok so ive had a go at another conversion problem to check im understanding what to do. The problem is convert 0.4 g/100cm³ to g/dm³ my solution is:

1dm³ = 1000cm³ so there is 1dm³ per 1000cm³

but since the origional units are in g/100cm³ the conversion factor is 1/(1000/100) = 0.1

therefore 0.4g/100cm³ * 0.1 = 0.04g/dm³

Is this correct? Thank You

No it is wrong.

If there are 0.4g in 100cm³ and 1 dm³ = 1000cm³ will there be 10times more or less in 1dm3 compared with 100cm3?  Now look at your answer.

[Luke149]

Ah so to convert from 100cm³ to m³ the conversion factor is 100cm³ * 1m³/1000000cm³ the cm³ cancel and you are left with 100/1000000 = x10^-4m³ therefore 0.0004 kg/100cm³ would be 4x10^-8kg/m³

and for the second problem, converting g/100cm³ to g/dm³ the conversion factor would be
1dm³ = 10cm³
so 100cm³ = 100cm³ * 1dm³ / 10cm³ = 10
therefor 0.4g/100cm³ = 4g/dm³

Is this correct?
Thanks for the help

[Borek]

Ah so to convert from 100cm³ to m³ the conversion factor is 100cm³ * 1m³/1000000cm³ the cm³ cancel and you are left with 100/1000000 = x10^-4m³ therefore 0.0004 kg/100cm³ would be 4x10^-8kg/m³

No. While you are right 100 cm³ is 10^-4 m³, you then multiply by the volume, instead of dividing.

0.4g
----
100cm³

We need two conversion factors, g -> kg

1kg
------
1000g

and cm³ -> m³

1m³
-------------
1000000cm³

and conversion looks like

0.4g x 1kg x 1000000cm³
--------------------------
100cm³ x 1000g x 1m³

g and cm³ cancels out. At this stage JUST CALCULATE the value, no further steps required.

1dm³ = 10cm³

No, 1 dm³ is not 10 cm³ (just like 1 m³ is not 100 cm³)

[Luke149]

Ok so for the conversion from 0.4g/100cm³ you get this which cancels down to

0.4g x 1kg x 1000000cm3
--------------------------
100cm3 x 1000g x 1m3

Which gives 0.4 x 10 x kg / m³ or 40 kg/m³

so for the conversion of g/100cm³ to g/dm³

you only need one conversion factor which is cm³ to dm³

1dm³
---------
1000cm³

so the conversion is

0.4g x 1000cm³
---------------
100cm³ x 1dm³

giving 0.4g x 10 / dm³ or 4 g/dm³

Does this make more sense?
Sorry its taking so long for mt to grasp this, thank you for the help

[Luke149]

Which gives 0.4 x 10 x kg / m³ or 40 kg/m³

Sorry this should be 4kg/m³

[Borek]

Twice OK.

Unless I am wrong, I am too tired to think clearly.

[Luke149]

Thank you so much for your help i used your method to do a couple of eample questions and got the correct answers so i think its all good