Seems the spreadsheet method is the most accurate. The other way is quite a bit more difficult as the volume needs to be added into the calculation, as such it would be a lot less accurate.
Copied from here:
http://www.gold-prospecting-wa.com/gold-in-quartz.html
Another Simpler Method to Calculate the Weight of Gold In Quartz
This method is also explained on the video at method 2.
What you need is;
A Set of Accurate Scales
A container for water that is big enough to take the rock you are weighing without spilling the contents.
A marker to mark the water container at the different water levels required.
The steps are -
Weigh the rock and record the dry weight.
Partially fill the water container with water and mark the level at the top.
Place the rock specimen in the container.
Mark the new level of the water on the side of the container.
Remove the rock and make sure all the water droplets are returned to the container.
Zero or tare the weight on the scales with the water container on it back to zero.
Fill the container up to the new level and record the weight of the water replaced.
Multiply that weight by the SG of the main matrix of the material. If it is quartz multiply it by the SG of Quartz 2.65.
Take that weight away from the dry weight of the rock and the weight left is a rough estimate of the gold in that specimen.
Remember, this is definitely not as accurate as the first method and both methods are only rough estimates - be cautious with their use.