[Uniq!]

Код:

procedure TForm1.Button1Click(Sender: TObject);
var
 art : string;
 num,col0 : integer;
begin
art := '00120';
col0 := Length(art) - Length(IntToStr(StrToInt(art)));
num := StrToInt(art);
Caption := IntToStr(num) + ' нулей:' + IntToStr(col0);
end;