Math Help - Converting kg/m3 to kg/mm3

1. Converting kg/m3 to kg/mm3

I have 7850 kg/m3

and its included in the following calculation

1,35*gk

where gk is = 30*120*7.85*10^-6 * 9,82
Another calculation i have seen writes 7,85 * 10^-1
30*120= mm²
7.85*10^-6 = kg/mm^3
9,82= N/kg

the answer To equation 1.35*gk= 0,375 N/mm
what actually drives me crazy is That i dont know how
7850 kg/m3 becomes 7,85*10^-6 or *10^-1 and still gives same answer
could Someone explain To me thoroughly and show me how
7850 kg/m3 is converted in this case

thank you

2. Re: Converting kg/m3 to kg/mm3

Your notation is extremely confusing. Equals signs denote equality. So, you are saying that 30*120 is equivalent to mm2. I think what you mean is $gk = \left( 30\cdot 120\text{ mm}^2\right)\left(7.85\cdot 10^{-6}\dfrac{\text{kg}}{\text{mm}^3}\right)\left(9.82 \dfrac{\text{N}}{\text{kg}}\right)$, so the units for $gk$ are $\dfrac{\text{N}}{\text{mm}}$. What calculation are you saying is equivalent?

3. Re: Converting kg/m3 to kg/mm3

You convert Kg/m^3 to Kg/mm^3 using the fact that there are 1000 mm per meter. Thus 1 meter = 1000 mm, and hence 1m/1000mm = 1. So you can multiply anything by 1m/1000mm and its just like multiplying by 1. Similarly, you can take the number 7.85x10^3 Kg/m^3, and multiply by 1^3 without changing its value:

$7.85 x 10^3 \frac {Kg}{m^3} = 7.85 x 10^3 \frac {Kg}{m^3} \times ( \frac {1 m}{ 1000 mm})^3 = 7.85 x 10^3 \frac {Kg}{m^3} \times \frac {1 m^3}{1000^3 \ mm^3} = 7.85 x 10^{-6} \frac {Kg}{mm^3}$

I trust you see how the m^3 terms canceled out. Hope this helps. I have no idea where the 7.85 x 10^-1 comes from; how did that come up?