How do I convert kg/m3 to g/cm3?

Question

The question was 3200kg/m3 = 3.2g/cm3. I don't understand the steps involved?

If you could provide a easy to remember logical explanation that would be great.

Answer 1

1 Kg = 1000g

Hence, 3200 kg = 3200 x 1000 g

1 m3 = 100x100x100 cm3 = 1000000 cm3

Hence 3200 kg/m3 = 3200 x1000 / 1000000 g/cm3 = 3.2 g/cm3

Answer 2

kg / m^3 * 1000 g/kg / (1000000 cm^3/m^3) = .0001 g/cm^3

Deal with the units (multiplying and dividing in numerator or denominator) and the numbers will come out right.

The units to go from kg/m^3 to g/cm^3 are as above, equivalent to

kg/m^3 * g/kg * m^3/cm^3.

As in normal fractional arithmetic, the m^3 and the kg "cancel out" leaving the desired units.  On then just inserts the individual conversion factors and the arithmetic will provide the correct answer as given above in the first line.

Answer 3

1 kg = 1000 g

1 m = 100 cm

Therefore, 1m3 = 100^3 cm3

Therefore, 1 kg/m3 = 1000/100^3 g/cm3

1000 = 10^3

and 100 = 10^2

Therefore,

1 kg/m3 = 10^3/10^6 g/cm3 (because (10^2)^3 = 10^6)

= 1/10^3 g/cm3

= 1/1000 g/cm3

So, to convert from kg/m3 to kg/cm3, divide by 1000.

3200kg/m3 = 3200/1000 g/cm3 = 3.2 g/cm3

Answer 4

first think about the top of the units: to go from kg to g you need to multiply by 1000.

the bottom units are slightly trickier: first to get from m to cm you multiply by 100, however when something is cubed or squared you need to cube or square the multiplication factor.

so therefore you have to multiply by

1000/100^3 = 1000/1000000 = 0.001

which is the same as dividing by 1000

Answer 5

Simply divide by 1000. This is easiest to remember. To convert from g/cm3 to kg/m3 just multipy by 1000

Answer 6

First of all 1 kg = 1000g and 1m = 100cm.

1m3 = volume of a cube of side 1m. or 100cm.

Therefore 1m3 = 100 x 100 x 100 cm3

                     = 1000000 cm3.

Now,  1kg/m3 = 1000g/1000000cm3    (as 1kg = 1000g and 1m3 = 100

                                                                       0000cm3)

      => 1kg/m3 = 1/1000 g/cm3.

Therefore 3200kg/m3 = 3200/1000 g/cm3

                               = 3.2 g/cm3.  

Answer 7

You can use dimensional analysis to convert units.

For example you have kg and you want grams, so

multiplying by (1000 g / 1 kg) is like multiplying by 1, and allows you to cancel the old units and get the ones you want.

To change from (1/m3) to (1/cm3), multiply by

(1m/100cm)^3.

3200 (kg/m3) = 3200 (kg/m3) * (1000g/1kg)

                     = 3200 * 1000 (g/m3)

                     = 3,200,000 (g/m3) * (1m/100cm)^3

                     = 3,200,000 (g/m3) * (1m3/(100cm)^3)

                     = 3,200,000 (g/1000000cm3)

                     = 3.2*10^6 / 10^6 (g/cm3)

                     = 3.2 g/cm3