When setting a fire, I find I usually create a small pile of kindling refuse and sawdust on the hearth. Rather than go in search of the vacuum cleaner, I’d prefer to use today’s invention: a draught-driven suction tube.
Set the draught to maximum for a few seconds and direct the (insulated) end of the flexible metal hose at the detritis in front of the fire.
This is sucked up into the chimney gas stream, burning the particles of dust and leaving the hearth area comparatively clean.