How Many Liters in a Gallon?

Date: 06/29/2002 at 21:21:44
From: Shannon
Subject: How many liters are in a gallon


I cant figure out how to convert liters to gallons. Can you help me? 
Here's an example: "If our pool is filled up with 500 gallons of 
water then how many liters would be in our pool?"

Date: 07/01/2002 at 08:27:01
From: Doctor Ian
Subject: Re: How many liters are in a gallon


Hi Shannon,

There's an easy way, and a hard way.  The easy way is to point 
your browser at a conversion calculator like the one at

    http://www.convertit.com/ 

You can type in '500 gallons' in the left-hand box, and 'liters' 
in the right-hand box, and the calculator will do the conversion 
for you. 

Of course, this doesn't teach you how to do the conversions 
yourself, if you're interested in learning that. 

The quick-and-dirty conversion looks like this:
  
  A liter is about the same as a quart. 

  There are 4 quarts in a gallon, so there are about 
  4 liters in a gallon.

  So there are about 4 * 500 = 2000 liters in a 500-gallon
  pool. 

But this is only good to about 10%.  So what it tells you is that 
the true answer is somewhere between 1800 and 2200 liters.  That 
might be good enough for your purposes, or it might not. 

But suppose you want a precise answer, and you don't have an 
Internet connection handy?  Then there are a few of facts that 
you'd need to have memorized:

  1. There are 2.54 centimeters in an inch.

  2. There are 231 cubic inches in a gallon.

  3. There are 1000 cubic centimeters in a liter.

If you know these facts, you can proceed this way.  If the pool 
contains 500 gallons, then it contains

            231 in^3
  500 gal * --------
            1 gal

cubic inches, and 

            231 in^3     2.54 cm
  500 gal * -------- * (--------- )^3
            1 gal          1 in   

cubic centimeters.  Note that I had to cube the whole conversion 
factor!  Forgetting to do this is one of the easiest ways to 
screw up a conversion like this. 

Now we're into the metric system, so we can use our final fact:

            231 in^3     2.54 cm        1 liter
  500 gal * -------- * (--------- )^3 * --------
            1 gal          1 in         1000 cm^3

Now we can put the numbers together, and the units together:

        231   2.54^3     1          in^3   cm^3   liters
  500 * --- * ------ * ---- * gal * ---- * ---- * ------
         1      1^3    1000         gal    in^3   cm^3

The units cancel out just the way numbers do:

                                     /      /
        231   2.54^3     1          in^3   cm^3   liters
  500 * --- * ------ * ---- * gal * ---- * ---- * ------
         1      1^3    1000    /    gal    in^3   cm^3
                                     /      /      /

leaving us with 

  500 * 231 * 2.54^3 / 1000 = 1893 liters.

This agrees with our quick-and-dirty estimate.  

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/