How do I convert kg/m3 to g/cm3 and understand the logic behind it?

AI Thread Summary
To convert kg/m³ to g/cm³, the process involves recognizing the relationship between the units. Specifically, 1 kg equals 1000 g, and 1 m³ equals 1,000,000 cm³. Therefore, when converting 3200 kg/m³ to g/cm³, you multiply by 1000 to convert kilograms to grams and divide by 1,000,000 to convert cubic meters to cubic centimeters, resulting in 3.2 g/cm³. The confusion arises from the fact that while a cubic meter is larger than a cubic centimeter, the density conversion requires division due to the volume change. Understanding these unit relationships clarifies why the final value decreases in this specific conversion.
Nellen2222
Messages
54
Reaction score
0

Homework Statement




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

3200kg/m^3 ---> 3.2g/cm^3


Homework Equations




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

The Attempt at a Solution



I know how to do dimensional analysis, but I just don't really understand the logic in this. I'll go step by step and please explain this to me it is crucial!


1) 3200kg/m^3 ----> g/cm^3

2) 3200kg/m^3 * 1000kg/1g*1m^3/1*10^-6cm^3 = 3.2kg/cm^3

I just don't understand why I divide g/m^3 by a million to reach g/cm^3. Isnt one cm^3 a smaller value(or area) than a m^3? Shouldn't I be multiplying by a million?

For instance: if I don't have a density and simply convert 100m^3 to 100cm^3 the answer is 100 000 000 cm^3. This makes sense because a metre is larger than a CM thus the value will be bigger .

So, Why is this not the case for when I have a density? Why do I have to divide by a million in order to go from m^3 to cm^3 in that case and ultimately reach a smaller value.

Please help me understand where my logic goes wrong.
 
Physics news on Phys.org
3200 kg m-3 = 3200 kg m-3 X 1000 g kg-1/ 100000 cm3 m-3
 
? what
 
Convert kg into g. (multiplying 1000 g per kg)

Convert cubic metre into cubic centimetre (dividing 1000000 cc per cubic metre)

Dimensions are matched, so we get the right answer.
 
The dimensions can match but the coefficiant(value in front) can be in either spot.. so technically can still have the wrong answer..
 
Man, they are correct. If you are adamant to make mistake, even God can't help it then. Using dimensions in coefficients helps us to determine if we are going on the right path.

Ask yourself - How many grams in a kilogram? How many cc in a litre -> how many litres in a cubic metre?
 
yeah- its all about 'ask yourself' - I just don't get why I am dividing by a million if a m^3 is bigger than a metre^3..
 
? What are you saying!? Isn't metre is shorted as m?
 

Similar threads

I Unit Conversions of Force: How to Convert Between Different Units of Force?
Replies
4
Views
1K
I Solve equation from dimensional analysis: 3 eq., 6 unknowns
Replies
1
Views
874
How Many Milligrams of Fluoride Are in 8 Cups of Water?
Replies
1
Views
5K
I Using Dimensional Analysis to derive an equation (Walter Lewin video)
Replies
5
Views
2K
How to Convert Lbm/ft^3 to kg/m^3?
Replies
9
Views
8K
How do I convert specific gravity of salt water to density and concentrations?
Replies
10
Views
4K
I Extremely strange consequence of the speed of heat value
Replies
19
Views
2K
How do I convert meters cubed to cubic centimeters?
Replies
4
Views
2K
How much force do I exert on the Earth?
Replies
6
Views
3K
How do I use the number of oscillations given?
Replies
18
Views
3K

Hot Threads

Recent Insights

Back
Top