The relative atomic mass of uranium is #238.0color(white)(l)"u"# , such that every mole of the atom has a mass of # 238.0color(white)(l)"g"#.
#30color(white)(l)color(blue)("mg")=30*color(blue)(10^(-3)color(white)(l)"g")=3.0*10^(-2)color(white)(l)"g"#
Hence the number of moles of Uranium atoms in a #30color(white)(l)"mg"# sample would be
#3.0*10^(-2)color(white)(l)color(red)(cancel(color(black)("g")))*(1color(white)(l)"mol")/(238.0color(white)(l)color(red)(cancel(color(black)("g"))))=1.26*10^(-4)color(white)(l)"mol"#
Each mole of any substance contains #6.023*10^(23)# particles. Therefore #30color(white)(l)"g"# of uranium would contain
#1.26*10^(-4)color(white)(l)color(red)(cancel(color(black)("mol")))*6.023*10^(23)color(white)(l)"atoms"*color(red)(cancel(color(black)("mol")))^(-1)=7.6*10^(19)color(white)(l) "atoms"#
