The property of metals that allows them to be rolled without breaking is ductility.

Here's a breakdown:

* Ductility is the ability of a material to deform under tensile stress without fracturing. This means the metal can be stretched or drawn into a thin wire without breaking.

* Malleability, a closely related property, refers to the ability of a metal to be hammered or pressed into thin sheets without breaking.

Both ductility and malleability are important properties that allow metals to be shaped and formed into useful objects.