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Conversions

# Conversions - Conversions Conversion factors are ways of...

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Conversions Conversion factors are ways of relating quantities or values of two differing units. Some examples of values that could be used as conversion factors would be: 2.54 centimeters = 1.00 inch 0.621 miles = 1.00 kilometer 1.00 quart = 0.946 liters 454 grams = 1.00 pound You can find more of these in your textbook. What is important is to learn how to use them to get from the value and unit you have been given to the value and unit that is desired. All of the above equalities can be rewritten as ratios. For example: 2.54 centimeters = 1.00 inch If we divide both sides of the equation by 1.00 inch 2.54 centimeters 1.00 inch = 1.00 inch 1.00 inch the result is 2.54 centimeters 1.00 inch = 1 We now have a conversion factor relating centimeters and inches. Note that we could just have easily divided both sides of the equation by 2.54 centimeters and the result would have been “flipped” but still equal to 1. The conversion factor is useful to change from one unit to another because anything you multiply by “1” is still the same value, even if it looks different. For the rest of this paper we will be using notations called “trees”. They are a way to keep units aligned to see more easily what goes where. The following is an example of the multiplication using fractions followed by the same multiplication in “tree” form. 5.00 inches = ? centimeters 12.7 centimeters = (5.00 inches) 2.54 centimeters 1.00 inch As the units become more complex, this form can become confusing and cumbersome. Below is the “tree” form of this calculation. It keeps the numerators (tops) and denominators (bottoms) more in line with each other to lessen confusion about what is multiplied and what is divided. 12.7 centimeters = 2.54 centimeters 1.00 inch 5.00 inches The trick is to put what you were given, or what you have , in the top left “box” and then line up units to cancel until the only unit left is the desired unit, or what you

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Conversions - Conversions Conversion factors are ways of...

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