Hardness is based on a gem-trade standard called the Mohs Scale, developed in the early 19th century. The higher the Mohs scale number, the harder the stone. Diamonds are rated the highest, at 10; rubies and sapphires are Mohs 9; emeralds and topaz, 8; and garnets, tourmalines and quartz, 7. Anything with a Mohs scale rating of 6 or less can be easily scratched, for example: coral, lapis lazuli, opal, pearl, chrysocolla, or turquoise. Gold, silver, and platinum have a rating of Mohs 2-1/2 to 4, meaning they require special care when wearing, storing, or cleaning. 
Mohs Scale of Hardness

1  Talc
2  Gypsum
3  Calcite
4  Fluorite
5  Apatite
6  Feldspar
7  Quartz (Amethyst)
6.5 - 7.5  Garnet
7.5  Beryl (Emerald)
8  Topaz
9  Corundum (Ruby and Sapphire)
10 Diamond


What the scale does not make obvious is that the numeric values assigned to each interval of hardness are not equal. Some stones are disproportionately harder than others:

Gemstone Mohs Rating Results from Grinding Test

Diamond

10

Approximately 90 times harder than corundum

Ruby/Sapphire (corundum)

9

Approximately 5 times harder than topaz

Topaz

8

Little difference between topaz and quartz

Emerald

7.5

Quartz

7
More information on mohs scale of hardness
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http://www.galleries.com/minerals/hardness.htm
http://chemistry.about.com/od/geochemistry/a/mohsscale.htm
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