How does this conversion work. kg/m^3 is equivalent to g/cm^3?

Question

How does this conversion work. kg/m^3 is equivalent to g/cm^3. The book says scientist use the g/cm^3 form which is equivalent because it is much smaller. I cant figure out how exactly that is equivalent. I see that it must be a 1000 times smaller since 1kg = 1000g, but 1 m is supposed to = 1000 mm. I dont understand their logic in this process. I know 1cm^3 is 0.000001m, but still dont get it. Can someone please show how to do this with work as well. Thanks

Thats what i thought, that it wasnt eqivalent, i wonder how they did that change then both those formuals for density are different

Answer 1

They are NOT equivalent !
kg/m³ and kg/litre are EQUIVALENT!

1 kg = 1000 g .....(I)

1m = 100 cm
1m³= 100³ cm³ = 1000000 cm³...(II)

Divide relation (I) by (II)

1 kg/1 m³ = 1000 g/1000000 cm³

1 kg/m³ = 0.001 g/cm³

Answer 2

If you have something you want to convert...make sure you write out all the units, when trying to convert it. Then cancel them, and you should be left with the units you are searching for. Example...

15 m^3
= 15(m)(m)(m)* (100 cm/m)(100cm/m)(100cm/m)

Notice that there are three m's in the numerator of that fraction, and there are three m's in the denominator. It looks like this now.

15(m)(m)(m)*(100cm)(100cm)(100cm)
----------------------------------------------------
(m)(m)(m)

Cancel out the m's...because meters divided by meters equals 1.

You are left with 15(100cm)(100cm)(100cm)
= 15*1000000cm^3
= 15,000,000cm^3

Do the same thing for the kg, and g.

The short way to convert a number like 15kg/m^3 to g/cm^3 would be...

[15(kg/m^3)]*[1000g/kg]*[(1m^3)/1000000cm^3)]
= 15*kg/kg*1000g*(m^3/m^3)/(1000000cm^3)
= 15g/1000cm^3
= .015 g/cm^3

If you could remember that for converting kg/m^3 to g/cm^3 was just to divide the number by 1000, and then change the units, you could do it. But I would suggest the long way until you become for fluent in conversions.

Answer 3

1 kg/m^3 = 1000g / 10^6 cm^3 = 10^-3 g/cm^3

we use g/cm^3 because it is very useful in calculating small masses, especially in Chemistry

Answer 4

In unit conversion, use the 'unit cancellation' method so u wont get lost.

1 m = 100cm
1m^3 = 1,000,000 cm^3



1kg/m^3 = 1kg/m^3 X 1m^3/1,000,000 cm^3 (cancel out m^3 unit)
= 1kg/1,000,000cm^3
* 1kg = 1,000g
= 1kg/1,000,000 cm^3 X 1,000g/1kg (cancel out kg unit)
= 1,000g/1,000,000cm^3
=0.001g/cm^3

NOT EQUAL...
1kg/m^3 = 0.001g/cm^3

Answer 5

It seems that this is to do with ratio which is: 10 : 1

1000g to 100cm
10 kg to 1 m

If you stay within the ratio it should be the same... I think/hope.