Metric Conversion Homework Help: Stumped by Division

[leroyjenkens]

Homework Statement

I have no idea how they got this answer. It says "doing the division gives you..." What division? It doesn't tell me what has been divided. The centimeters into grams? I can't find any plausible division that would give me .002 for an answer. I've been staring at this for an hour.

 

[jhae2.718]

It's basic dimensional analysis. The unit conversion factors used are:
1 kg = 1000 g
1 m= 100 cm thus 1 m³ = 1 x 10⁶ cm³

Multiply/divide the original expression by these factors so that the kg and m units cancel out and you'll get the answer shown.

 

[leroyjenkens]

It's basic dimensional analysis. The unit conversion factors used are:
1 kg = 1000 g
1 m= 100 cm thus 1 m³ = 1 x 10⁶ cm³

Multiply/divide the original expression by these factors so that the kg and m units cancel out and you'll get the answer shown.

Thanks for the reply.
I keep coming up with .02 as an answer, not .002. I must be setting up the multiplication/division equation wrong.
I multiply the 1000g times 20kg to get 20,000g and divide it by 10^6 centimeters?

 

[jhae2.718]

Actually, I think their answer is wrong. I get the same answer as you do. Here is the same problem done by Wolfram Alpha: http://www.wolframalpha.com/input/?i=20+kg%2Fm^3+in+g%2Fcm^3

 

[collinsmark]

Thanks for the reply.
I keep coming up with .02 as an answer, not .002. I must be setting up the multiplication/division equation wrong.
I multiply the 1000g times 20kg to get 20,000g and divide it by 10^6 centimeters?

I think you are doing it correctly. Problem with book's answer.

 

[Redbelly98]

Google gets 0.02 g/cm^3 as well:
http://www.google.com/#hl=en&source=hp&q=20+kg/m^3+in+g/cm^3&aq=f&aqi=h1&oq=&fp=c26c79a56c95bda8

I think "doing the division" means dividing by 1000. But conceptually, it may be easier to think of it as multiplying by 1000 (to convert the mass units), and then dividing by 10^6 (to convert the volume units).