SOLUTION: I am the dad here and frustrated I can't help my son with this problem. It reads: If 1.0 km cubed of air has mass 1,200,000,000 kg, what is the density of air in g/cm cubed? The a

Algebra ->  Customizable Word Problem Solvers  -> Unit conversion -> SOLUTION: I am the dad here and frustrated I can't help my son with this problem. It reads: If 1.0 km cubed of air has mass 1,200,000,000 kg, what is the density of air in g/cm cubed? The a      Log On

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Question 153128: I am the dad here and frustrated I can't help my son with this problem. It reads: If 1.0 km cubed of air has mass 1,200,000,000 kg, what is the density of air in g/cm cubed? The answer is given as 1.2x10 to the negative 3 g/cm cubed. We know the equation is density equals mass/volume but we obviously are missing something in the "power of" and the ending up with a negative power in the answer. I think we got the conversions correct, but am not even sure of that now. My son and I have worked on this (what appears to be a) simple math problem for over an hour and cannot explain the steps on getting to the answer given. I'm ashamed to admit we're both snowed. Any help would be appreciated. This is from a worksheet and I have no idea if it is from a textbook.
Found 3 solutions by jim_thompson5910, ankor@dixie-net.com, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember,

1 kg = 1000 g or 1 kg = 1*10^3 g

and

1 km = 1000 m = 100,000 cm or 1 km = 1*10^3 m = 1*10^5 cm


So 1,200,000,000 kg = 1,200,000,000,000 g or 1,200,000,000 kg = 1.2*10^12 g


and 1 km^3 = (100,000)*(100,000)*(100,000) cm^3 = 1,000,000,000,000,000 cm^3 = 1*10^15 cm^3


-----------------------------

So

1,200,000,000 kg = 1.2*10^12 g

and

1 km^3 = 1*10^15 cm^3


----------------------------------

Also, remember that 

 
            Mass
Density =  ---------
            Volume


which is symbolically

D=M%2FV




D=M%2FV Start with the given equation.



D=%281.2%2A10%5E12%29%2F%281%2A10%5E15%29 Plug in the given mass M=1.2*10^12 g and the given volume V=1*10^15 cm^3


D=1.2%2A10%5E%2812-15%29 Divide 1.2 by 1 to get 1.2. Divide 10%5E12 by 10%5E15 by subtracting


D=1.2%2A10%5E%28-3%29 Subtract the exponents.


So the density is 1.2%2A10%5E%28-3%29 g/cm^3

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I am the dad here and frustrated I can't help my son with this problem. It reads: If 1.0 km cubed of air has mass 1,200,000,000 kg, what is the density of air in g/cm cubed?
:
1,200,000,000 = 1.2(10^9)
:
Convert the mass: 1.2(10^9) kg to grams:
1.2(10^9) * 10^3 = 1.2(10^12) grams
:
To convert 1 cu km to cubic cm
First:
1 km = 10^3 meters = 10^5 cm
then
Find the volume of a cube with sides of 10^5 cm: (10^5)^3 = 10^15 cu/cm
:
Dens = %281.2%2810%5E12%29%29%2F%2810%5E15%29 = 1.2%2810%5E%28%2812-15%29%29%29 = 1.2%2810%5E-3%29 grams/cu cm
;
Did this help?

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If 1.0 km cubed of air has mass 1,200,000,000 kg, what is the density of air in g/cm cubed? The answer is given as 1.2x10 to the negative 3 g/cm cubed.
--------------------
Comment: The key is to properly change (km)^3 to (cm)#.
(km)^3 = (1000m)^3 = (1000*100cm)^3 = (10^5cm)^3 = 10^15cm^3
(1.2x10^9 kg/1.0 km^3)(1000g/1kg)[(km)^3/(10^15cm^3)]
----------
Cancel the units to get g/cm^3
Evaluate the quantities as follows:
[1.2x10^9 * 1000 * 1] / [1.0 * 1 * 10^15] = [1.2*10^12]/[10*15] = 1.2x10^-3
-----------
Final answer 1.2x10^-3 g/cm^3
=======================
Cheers,
Stan H.