A miner claims his gold nugget is pure gold. It has a mass of 111.1 g and a volume of 10 ml. Do you believe him? Why or why not?

(111.1 g) / (10 mL) = 11.11 g/mL

The density of pure gold is 19.30 g/mL, so I don't believe him.

(Although I was skeptical from the beginning, since real miners make a point of saying nothing about their strikes.)

Gold nuggets usually contain small quantities of quartz & other minerals.

D of the miner's nugget = 11.11 g/mL = 11.11 g/cm^3

.... now look up the density of gold and see if it is the same

That sounds more like fools gold.