Proportion - Conversion Factors

Proportion - Conversion Factors

Conversion factors will always give you the right answer when trying to convert from one unit to another

• 1 inch = 2.54 centimeters

• 1 foot = 12 inches

What is the key?

• Could you think of a different format to write the conversion?

•  $\frac{1\ inch}{2.54\ centimeters}\ =\ \frac{2.54\ centimeters}{2.54\ centimeters}=1$  

• 1 is the key for all our problems

A few examples

• 180 centimeters -> feet?

•  $180\ centimeters\ =\ 180\ centimeters\ \cdot\ 1\$  

•  $=\ 180\ centimeters\ \cdot\ \frac{1\ inch}{2.54\ centimeters}\cdot\frac{1\ foot}{12\ inches}\approx5.9\ feet$  

• cancel the original unit to approach the unit we want

Given that 1 inch is 2.54 centimeters and 1 ounce is 28.35 grams, convert 16.2 in² oz^-1to centimeters and grams

• Hint: inch -> centimeter, oz -> grams

• Answer: $\approx3.686\ cm^2g^{-1}$