It helps to memorize approximate density values for the main fiber types. Generally: Cellulosics (cotton, rayon)>Protein (silk, wool)>Synthetics (polyester>nylon>acrylic>polypropylene>polyethylene).
Step 1: Approximate Densities:
Polyester (PET): ~1.38 g/cc
Cotton: ~1.54 g/cc
Wool: ~1.31 g/cc
Nylon 6,6: ~1.14 g/cc
Polyethylene: ~0.95 g/cc
Step 2: Comparing Densities: Polyester has a density less than cotton but greater than wool. It's denser than both nylon and polyethylene.