# Dr. Bill's Conversion System

Copyright, 1995 - Dr.F.W. Boyle, Jr.
A large part of experimentation and research in Chemistry involves the use of conversion factors to transform numbers from one measurement system to another. The actual conversions are generally simple but determining the "conversion factor" can be complicated.

The method described herein uses the "to"/"from" method. The actual origins of this methods are vague. Perhaps it comes from years of learning. It was developed to aide the student, professor, and researcher in using commonly available information to convert any measurement from one system into any other system.

Where can one find conversion factors ? Today, most food and product packages contain listing for both the English and the metric system of measurements. One can use the numbers given on these product to develop "conversion" factors. An example is the volume of cola in a can of soda pop.

From the label one finds the can contains 12 fl (fluid ounces) or 355 milliliters. The relationship is set up thusly:

12 ounces = 355 milliters

Some terms which are commonly used mean the same while at the same time sounding different. A good example is that used for measuring volumes.

1 milliliter of water = 1 cc of water = 1 cubic centimeter of water

TABLE OF COMMON EQUALITIES:

```1 inch = 2.54 centimeter    12 inches = 1 foot    3 feet = 1 yard

1 meter = 100 centimeter     1 centimeter = 10 millimeter

1 lb = 453.6 grams     1 lb = 16 ounces

1 kilogram = 1000 grams      1 gram = 1000 milligrams

1 quart = 0.946 liters   2 pints = 1 quart    4 quarts = 1 gallon

1 liter = 1000 milliliters
```
DENSITY: Density is both a physical parameter used to identify materials and a basic conversion factor. Density is most often expressed as grams per cubic centimeter (cm3). Under the SI system, density is to be expressed in kilograms per cubic meter.

Water has a density of 1 gram per cubic centimeter (1 g/cm3). This relationship can be written in the following format.

1 gram H2O = 1 cubic centimeter H2O

Density expressed in this format can be used to convert between mass and volume.

Dr. Bill's "to"/"from" Conversion System: Converting systems is as simple as knowing where you are going "to" and where you are coming "from". The "to" is the unknown value and its unit. The "from" is the known value and its unit.

For example, let's convert 1 yard to centimeters.

First, yards need to be converted to feet. So ...

1 yard = 3 feet
So we are going "to" feet "from" yards. Place the "to" over the "from" in a fraction format as follows.

```                    "to"          3 feet
over          ------
"from"         1 yard
```
Had we wanted to convert "from" feet "to" yards, the factor would have been formed thus:

```                     "to"         1 yard
over         ------
"from"        3 feet
```
As one can see, the "to" is placed over the "from" for this conversion factor. By following the "to" over the "from" convention, factors to transform values between different measurement systems can be easily developed. All the is needed is an equality expression like those presented above.

To continue our original operation, multiply the original amount by the "factor":

```                              3 feet
1 yard x  ------
1 yard
```
Since we have a common term in both the numerator and the denominator, these can be cancelled (just the term not the numerical value). So we are left with:

```
1  x  3 feet
------
1
```
Finish multiplying and dividing to get the answer of 3 feet.

Next the conversion "from" feet "to" inches needs to be made. Use the equality given above.

12 inches = 1 foot
The "to" over the "from" format gives:

```                            12 inches
---------
1 foot
```
for the factor. Multiply the number of feet by this factor as is shown below, cancelling common terms.

```                          12 inches
3 feet x  ---------
1 foot
```
or

```                           12 inches
3 x  ---------    =  36 inches.
1

```
Lastly use the inch to cm equality to produce the final conversion factor. Use Dr. Bill's "to" over "from" method.

```                   "to"         2.54 cm
over         -------
"from"        1 inch
```
Then multiply 36 inches by this factor to get the final answer.

```                             2.54 cm
36 inches x  -------
1 inch
```
Inches cancel leaving us with:

```                              2.54 cm
36 x  -------   =   91.54 cm
1
```
The "to" over "from" method works for any conversion. As one's ability inproves multiple steps may be written as one as in the following example.

```
3 feet     12 inches      2.54 cm
1 yard  x  ------  x  ---------  x   -------
1 yard       1 foot       1 inch

```
Now let's work some conversions.

A) Convert 3 ounces to milliliters

B) Convert 1 pound of water to kilograms of water

C) Find five different unit conversions on goods that you have or might purchase. An example is the soda can above.