A ranking, not a ruler
Friedrich Mohs set the scale out in 1812 by choosing ten minerals where each scratches the one below it. That is all it measures: what will and will not scratch what. It is ordinal, which means the numbers put minerals in order and nothing more — the intervals between them are not equal and were never meant to be.
The gap that makes this concrete is the top one. Diamond at 10 is several times harder than corundum at 9 in absolute terms, while the step from talc at 1 to gypsum at 2 is negligible by comparison. Any chart that draws the scale as evenly spaced bars implies a proportionality that does not exist, which is why the ranking rather than the spacing is what is shown here.
Seven is the number that matters in practice
Ordinary household dust is largely quartz, which sits at 7. Anything softer is being very lightly sanded every time it is wiped, handled or put in a pocket. That is why softer stones in rings go dull long before they go anywhere near chipping — the damage is thousands of invisible scratches rather than one accident.
This puts a practical line under the stones suited to daily wear on a hand. Diamond, corundum in both its forms, spinel, topaz, tourmaline and quartz sit at or above it. Opal, moonstone, tanzanite, peridot, pearl and amber sit below, and are better suited to earrings, pendants and occasional wear where they meet less friction.
Hardness is not toughness
These are different properties and they frequently run in opposite directions. Hardness resists scratching. Toughness resists breaking. Diamond tops the hardness scale and will still cleave if struck along the wrong plane, which is precisely how diamond cutters have shaped it for centuries. Jade is far softer and famously hard to break — it was used for axe heads.
Emerald is the case that catches people out. At 7.5 to 8 it is hard enough on paper, but emeralds are usually heavily included, and those inclusions are fracture planes. An emerald can survive dust indefinitely and still split on a knock a softer, cleaner stone would shrug off.
So a high number does not mean a stone is safe in a ring, and a low one does not mean it will shatter. Read the number as one specific fact about scratching, and treat setting, wear pattern and inclusions as separate questions.