Density of water-- What should I do to get from 1000kg/m³ to 1g/cm³

I've been told those are two ways of writing water's density value. Thing is, if you divide 1000/1000 you get 1, but if you divide 1m³ per 1000 you get 1mm³ (instead of cm³, as stated).

So, what is the calculation to get from 1000kg/m³ to 1g/cm³?

1 kg = 1000 g
1 m³ = 100 x 100 x 100 = 1000000 cm³

1000 kg/m³ = 1000 x 1000 / 1000000 = 1 g/cm³

Another way to convert from kg/m^3 to g/cm^3 is as follows.

To pass from (1/m^3) to (1/cm^3), you have to multiply by (1m/100cm)^3 = [1m^3/(100cm)^3]

1000 (kg/m^3) = 1000 (kg/m^3)*(1000g/1kg) =

= 1000*1000 (g/m^3) =

= 1,000,000 (g/m^3)*(1m/100cm)^3 =

= 1,000,000 (g/m3)*[1m^3/(100cm)^3] =

= 1,000,000 (g/1,000.000cm^3) =

= 1,000,000g/1,000,000(cm^3) = 1 g/cm^3

Bye,

C6H6