[PsychoSoldier]

Hello, I just signed up to the forums because my girlfriend who is in a Chemistry class at U of I is being stumped by a problem.  The problem is in a program where you plug the answer in and it tells you whether that answer is correct or not. 

The problem asks to convert 16.3 g/cm^3 into lbs/ft^3.  According to the program, the answer is 1.02 x 10^3, which we were able to find out by using a conversion calculator on Google(16.3 g/cm^3 = 1 017.57576 lbs/ft^3).  We understand how to do conversion if it's something simple like cm to mL(1 cm = 1 mL), but in this case, 1 cm = .0328084 ft.  We try dividing 16.3 by 453.59(g to lbs) and dividing by .0328084, which gives us 1.095315117.  The issue we're having is no matter what math we do, we can't get that information to give us the correct answer.

So what steps are we missing?  How do we go about finding how many lbs per ft^3 when raising .0328084 ft to 1 ft?  There must be some kind of simple equation or process that we're missing out on, and no matter where we look on the internet, we can't find the answer for such a complex version of a density conversion problem.  This is stressing out my girlfriend terribly and is stressing me out because I'm trying to help her understand so she can go through the course with minimal difficulty.  Any help will be appreciated.

Cheers.

[sjb]

So what steps are we missing?  How do we go about finding how many lbs per ft^3 when raising .0328084 ft to 1 ft?

How many cubic inches are there in a cubic foot, for instance?

[PsychoSoldier]

So what steps are we missing?  How do we go about finding how many lbs per ft^3 when raising .0328084 ft to 1 ft?

How many cubic inches are there in a cubic foot, for instance?

12, of course.

[sjb]

No, there are not 12. There are 12 inches in a foot, but a cubic foot is a box with dimensions 1 foot x 1 foot x 1 foot, or 12 inches x 12 inches x 12 inches, or how many cubic inches?

[PsychoSoldier]

Ahhhh, then 1728 cubic inches.  That's the root of our problem, isn't it?

EDIT:  After relaying the information, my girlfriend was able to get it right.  I feel like an idiot for not considering that.  I was assuming since all the volume measurements were in cubic measurement, that the numbers would scale to be the same conversions.  Thanks so much for the help and quick response.  Have a great night.

[Borek]

This is about scaling - surface scales as a square on the length, volume scales as a cube of the length.

And in general, scaling (AKA https://en.wikipedia.org/wiki/Power_law) is one of the basic concepts in science.

[TheMantis]

You need to write your units down on paper and cancel out units.  Doing it on paper will minimize errors.

Here is the formula:

(16.3 g/cm3)x(0.0022046 lbs/g)x(1 cm3/0.0000353ft3)=1017.98810 lbs/ft3 = 1.02 x 10*3 lbs/ft3