How are the trans-decalin and cis-decalin structures numbered? Explain the steps involved in the IUPAC nomenclature for these fused ring systems.

The counting starts from one of the two bridgehead carbons. These are the two carbon atoms that are shared by both fused rings.

The numbering proceeds around one ring first, then continues to number the remaining carbons in the second ring. This convention ensures that the bridgehead carbons are typically assigned the numbers C-1 and C-6. The specific direction (clockwise or counter-clockwise) around each ring is chosen to give the lowest possible numbers to any substituents present; in the absence of substituents, it follows a sequential path around the rings.

• Counting starts from: One of the two bridgehead carbons.
• Direction: Around one ring, then continuing to the other ring.