SOLUTION: Could someone please help me with a math problem. I need to find out this problem. 1/5 of a gallon is ___ml. I am not sure on how to even start to convert it. Thanks for your t

I personally suspect you are trying to compare the
old "fifth of whiskey" which was 1/5 of a gallon before
the measures of alcoholic beverages went to the metric
ayatem, with the 750 milliliter bottle, still called a
"fifth", replacing the fifth of a gallon whiskey bottle.
You are wanting to know how the old "fifth" bottle 
compares with the new 750 ml. bottle of booze.  I can 
see you are very interested in whiskey. You are either a whiskey
corporation executive or a lush. J Kiddin'. 

The US gallon is defined as EXACTLY 231 cubic inches.
The inch is defined as EXACTLY 2.54 centimeters
The milliliter is EXACTLY the same thing as a cubic 
centimeter.

We begin with  of a gallon which can be 
written as

1 gal
------
   5

Next we multiply that by a fraction that has "gallon" on the
bottom so it will cancel out the word "gallon" in the top.
But we must be sure to put a new unit on top, so we will 
put cubic inches or in³ in the top.  Since we know that
the US gallon is defined as EXACTLY 231 cubic inches, we 
will put 1 gallon on the bottom and 231 in³ on the top

1 gal     231 in³
------ x ---------
   5       1 gal

Now the gallons will cancel:

1 gal     231 in³
------ x ---------
   5       1 gal

Next we need to cancel away the in³.  Since we know that
The inch is defined as EXACTLY 2.54 centimeters, we
know that 1 in³ equals (2.54 cm)³ or 2.54³ cm³ or 
16.307064 cm³.

So we multiply by a fraction with 1 in³ on the bottom and
16.307064 cm³ on top:

 1 gal     231 in³     16.387064 cm³
------- x --------- x -------------
   5        1 gal         1 in³

Now the in³'s will cancel:

 1 gal     231 in³     16.387064 cm³
------- x --------- x --------------
   5        1 gal          1 in³

Now all we need do is get rid of the cm³
Since we know that the milliliter is EXACTLY 
the same thing as a cubic centimeter, we
multiply by a fraction that has cm³ on the 
bottom to cancel away the cm³ on the top.

So we put 1 cm³ on the bottom and 1 ml on top,
and multiply by that fraction:

 1 gal     231 in³     16.387064 cm³    1 ml
------- x --------- x -------------- x -------
   5        1 gal          1 in³        1 cm³ 

Now the cm³'s will cancel:

 1 gal     231 in³     16.387064 cm³    1 ml
------- x --------- x -------------- x -------
   5        1 gal          1 in³        1 cm³ 


Now we multiply all the numbers together on top
and multiply all numbers on the bottom, and the
answer will be in ml (milliliters) because that
is the only unit that hasn't been canceled out:

 1 gal     231 in³     16.387064 cm³    1 ml      3785.411784 ml
------- x --------- x -------------- x ------- = ----------------
   5        1 gal          1 in³        1 cm³         5

= 757.0823568 ml.

So, as you can see, the new metric "fifths" contain about 7 ml.
less booze than the old "fifths".

Edwin