Number of nanoparticles in 1 gram?

Here is an example:

Gold (Au) Nanoparticles / Nanopowder (Au, 99.95+%, 15 nm)

For US1054, Number of nanoparticles in 1 gram=2.929 x 10¹⁶
Density of Au is 19.32 g/cm³
Volume of 1 gram Au = 1/19.32=5.176x10^-2 cm³
For spherical nanoparticles of 15 nm, volume of one particle = 4/3 x Pi x (7.5 x 10^-7)³ cm³ = 1.767 x 10^-18 cm³
Therefore, number of nanoparticles in 1 gram = [5.176 x 10^-2]/[1.767 x 10^-18] = 2.929 x 10¹⁶ nanoparticles