Using Julia, how to format Avogadro's Constant (or other numbers) in engineering notation?

Use the NumericIO.jl package

julia> using NumericIO

julia> const Avogadro = 6.022140857e23;

julia> formatted(Avogadro, :ENG, ndigits=4, charset=:ASCII)
"602.2E21"

julia> formatted(Avogadro, :ENG, ndigits=4)
"602.2×10²¹"