What is 12g/cm3 converted into kg/m3?

Question

Using the prefix conversion only, how to solve it through dimensional analysis?

Answer 1

I hope that helps AND thank you for watching!

Answer 2

We can split the top and bottom up separately then just combine them afterwords.

It's also important to know that there's 1000g = 1 kg

and there are 100cm = 1m, but since they want cm^3 to m^3, we cube both sides to get that

(100cm)^3 = (1m)^3

1,000,000 cm^3 = 1m^3

So now we can start with the dimensional analysis.

12 g ( 1 kg / 1000 g) = 0.012

Remember to put the value you want on the top. So we want to convert to kg, so it's 1kg/1000g rather than 1000g/1kg

1 cm^3 ( 1 m^3 /1,000,000 cm^3) = 0.000001 m^3

so puttin the top and bottom together we have 0.012kg/0.000001 m^3 =

12,000 kg/m^3