How do jewelers define the purity and hardness of a gold piece?

Purity and hardness of a piece of gold-mostly jewelry-is determined by how many carats (or karats) the gold piece contains. The following lists the gold percentages:

gold

24 Carat =100.0 percent pure
18 Carat =75.00 percent pure
14 Carat =58.33 percent pure
12 Carat =50.00 percent pure
10 Carat =41.67 percent pure
9 Carat =37.50 percent pure