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### 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/
```
Associated Topics:
Middle School Terms/Units of Measurement

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