The Moh's (Mohs) scale of hardness is the most common method used to rank gemstones and minerals according to hardness. Devised by German mineralogist Friedrich Moh in 1812, this scale grades minerals on a scale from 1 (very soft) to 10 (very hard). Because the Mohs scale is a relative scale, the difference between the hardness of a diamond and that of a ruby is much greater than the difference in hardness between calcite and gypsum. As an example, diamond (10) is about 4-5 times harder than corundum (9), which is about 2 times harder than topaz (8). Individual samples of a mineral may have slightly different Mohs ratings, but they will be near the same value. Half-numbers are used for in-between hardness ratings.
How to Use the Mohs Scale
A mineral with a given hardness rating will scratch other minerals of the same hardness and all samples with lower hardness ratings. Gems are examples of minerals. Gold, silver, and platinum are all relatively soft, with Mohs ratings between 2.5-4. Since gems can scratch each other and their settings, each piece of gemstone jewelry should be wrapped separately in silk or paper. Also, be wary of commercial cleaners, as they may contain abrasives that could damage jewelry.
I've added a few common household items to the basic Mohs scale to give you an idea of how hard gems and minerals really are and for use in testing hardness yourself.