Proportion - Conversion Factors

1 inch = 2.54 centimeters

1 foot = 12 inches

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

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

Hint: inch -> centimeter, oz -> grams

Answer: $\approx3.686\ cm^2g^{-1}$