[agrobert]

x mg/cm² [1 g / 1000 mg][1 kg / 1000 g][100 cm/1 m]² = x [CONVERSION FACTOR] kg/m²

Work to convert one unit at a time in steps and make sure units cancel. 

Follow red (mg --> kg) and blue (cm² --> m²) *this conversion is squared because it is cm² --> m²
[/quote]

Cancelling Units

x mg/cm² [1 g / 1000 mg][1 kg / 1000 g][100 cm/1 m]² = x [CONVERSION FACTOR] kg/m²

[agrobert]

Thanks Borek 

[JonathanEyoon]

x mg/cm² [1 g / 1000 mg][1 kg / 1000 g][100 cm/1 m]² = x [CONVERSION FACTOR] kg/m²

Work to convert one unit at a time in steps and make sure units cancel. 

Follow red (mg --> kg) and blue (cm² --> m²) *this conversion is squared because it is cm² --> m²

Cancelling Units

x mg/cm² [1 g / 1000 mg][1 kg / 1000 g][100 cm/1 m]² = x [CONVERSION FACTOR] kg/m²
[/quote]


I'm honestly still not following.  Is there an easier way to break it down  .  This really frustrates me.  I'm trying to use the factor label method, but it seems like we're converting two different things and I'm not clear on how to do that exactly, Especially how you get from cm^2 to m^2

[Padfoot]

Especially how you get from cm^2 to m^2

1 m²= 100cm x 100cm (length x width) = 10000cm² 

[JonathanEyoon]

ok how about from cm^3 to dm^3?


I can't understand the math of how you were able to get that.

I understand that 1 meter^2 = 100 cm x 100 cm. which equals 10,000 cm which is 1 meter^2.  Buy why would you say 10,000cm^2?  Doing that would make it equal to 100,000,000 cm.  which does not equal to 1 meter^2.  See my confusion here?

[Alpha-Omega]

The density of Benzene is 0.879 g/mL. Calculate the mass in grams of 1.00 qt of Benzene."

You are given 0.879 g/mL benzene.
You need g/qt of benzene.

Always begin with what you know.

0.879 g/mL

You need a conversion factor for mL to quarts.  So from the conversion table at:  http://www.sciencemadesimple.com/metric_conversion_chart.html

You find 1 mL = 0.034 fl oz
1 US quart = 32 fl oz 

(Please note I make a distinction about US quart because this is not the same in Imperial designations)

This is how you set up the equation:

(0.879 g/mL) x (1mL/0.034 fl oz) x (32 fl oz/1 quart)

The mL cancel out of the equation.
The fl oz cancel out of the equation.

And you are left with g/quart.

When you do the calculation you get:  827.29 g/quart = 827 g/quart.


Now you question about cm^3 and dm^3...this is where learning conversion is important...where the tables become useful:

1 cm^3 = 1 mL
1000 mL = 1 L
1L = 1 dm^3

This is a cubic decimeter and is a unit of volume NOT a unit of length..

Like a cubic centimeter is a unit of volume.

Are yiou getting it???

Cubic decimeters are used in Physical Chemistry  it is a common unit of measure for VOLUME.  Often used for the volume an amount of gas occupies.

You have to recognize anything cubed is a volume...like think of a rubix cube....a cube is 3 dimensional and has a volume...

Something squared ia an area....like an area rug in your home....anything squared ai an area L x W is a squared area.

Anything cubed has a volume.

[Alpha-Omega]

So since you are converting from cm^3 to dm^3

I already stated:

1 cm^3 = 1 mL

1000 mL = 1 L

so then 1000 cm^3 = 1 L

since 1 dm^3 = 1 L

then 1000 cm^3 = 1 dm^3

[Padfoot]

I can't understand the math of how you were able to get that.

I understand that 1 meter^2 = 100 cm x 100 cm. which equals 10,000 cm which is 1 meter^2.  Buy why would you say 10,000cm^2? 

10000 comes from 100 x 100, cm² comes from cm x cm.

EDIT: There is a difference between 10000²cm and 10000cm²

[Alpha-Omega]

OK...let me try it this way:

a cm is a unit of length
a m is a unit of length
a dm is a unit of length
a mm is a unit of length

When you cube any of these they become VOLUMES

cm x cm x cm = cm^3 = volume
m x m x m = m^3  = volume
dm x dm x dm = dm^3
mm x mm x mm = mm^3 = volume

When you square any of these they become AREAS

cm x cm = cm^2 = area
m x m = m^2 = area
dm x dm = dm^2 = area
mm x mm = mm^2 = area

If we are still on how to go from cm^2 to M^2

100 cm = 1m

(100 cm)^2 = 1 m^2  (you have to square the entire quantity)

100 x 100 = 10,000 then tag on the units cm^2

So this gives you 10,000 cm^2 = 1 m^2

[JonathanEyoon]

ok I think i'm actually starting to get it now.  I was just really, really, REALLY confused about the cubic and square values.


When it comes to Volume,

so dm^3 = 1 Liter

cm^3 = 1 milliliter


I have a question. So it'll take 1000 milliliter's to equal one Liter, so does this mean it'll take 1000cm^3 to equal one dm^3?

[Alpha-Omega]

WOO HOO...YOU GOT IT!!!!!!

I had the same problem when I was learning it...so do not worry...as you were writing...I began to see what you did not get...it is the meaning of the conversion that you need to get....and now you are on your way...GOOD JOB!!!!!

Let me know if you need more help/explanation...what you just wrote is 100% Correct....

1000 mL = 1L
1000 mL = 1000 cm^3
1000 cm^3 = 1 L
1L = 1 dm^3
so YES 1000 cm^3 = 1dm^3

so you now see:  1000 mL = 1000 cm^3 = 1L = 1dm^3 

they are all equal and all a conversion of one unit to another

And that is the way you will get it!!!!!! Good For You!!!!