0 4 5 8

All 100 targets have a solution.

\(1 = ( 458 \cdot 0 )!\)
\(2 = 50 - 48 \)
\(3 = 4 - 58^{0 }\)
\(4 = \frac{ 480 }{ 5 ! }\)
\(5 = 48 \cdot 0 + 5 \)
\(6 = 48^{0} + 5 \)
\(7 = \frac{ 840 }{ 5 ! }\)
\(8 = 45 \cdot 0 + 8 \)
\(9 = 45^{0} + 8 \)
\(10 = \frac{ 40 }{ 8 } + 5 \)
\(11 = \frac{ 5! }{ 40 } + 8 \)
\(12 = \frac{ 80 }{ 5 } - 4 \)
\(13 = 0 \cdot 4 + 5 + 8 \)
\(14 = 8^{\sqrt{4}} - 50 \)
\(15 = \frac{ 80 }{ 4 } - 5 \)
\(16 = \frac{ 40 }{ 5 } + 8 \)
\(17 = \frac{ 50 }{ \sqrt{4} } - 8 \)
\(18 = 58 - 40 \)
\(19 = 4 \cdot 5 - 8^{0 }\)
\(20 = \frac{ 80 }{ 5 } + 4 \)
\(21 = \frac{ 50 - 8 }{ \sqrt{4 } }\)
\(22 = \sqrt{485 - 0 !}\)
\(23 = 4! - 58^{0 }\)
\(24 = \sqrt{580 - 4 }\)
\(25 = \frac{ 40 \cdot 5 }{ 8 }\)
\(26 = 80 - 54 \)
\(27 = 40 - 5 - 8 \)
\(28 = ( 0 + 4 ) \cdot 5 + 8 \)
\(29 = \frac{ 50 + 8 }{ \sqrt{4 } }\)
\(30 = \frac{ 58 }{ \sqrt{4} } + 0 !\)
\(31 = 4 \cdot 8 - 5^{0 }\)
\(32 = \frac{ 80 \cdot \sqrt{4} }{ 5 }\)
\(33 = \frac{ 50 }{ \sqrt{4} } + 8 \)
\(34 = 84 - 50 \)
\(35 = 80 - 45 \)
\(36 = 45 - 0! - 8 \)
\(37 = 40 + 5 - 8 \)
\(38 = 50 - 4 - 8 \)
\(39 = 5 \cdot 8 - 4^{0 }\)
\(40 = \sqrt{40 \cdot 5 \cdot 8 }\)
\(41 = 4^{0} + 5 \cdot 8 \)
\(42 = 48 - 0! - 5 \)
\(43 = 40 - 5 + 8 \)
\(44 = 45 - 8^{0 }\)
\(45 = 85 - 40 \)
\(46 = 8^{0} + 45 \)
\(47 = 48 - 5^{0 }\)
\(48 = 0 \cdot 5 + 48 \)
\(49 = 5^{0} + 48 \)
\(50 = \sqrt{50^{\frac{ 8 }{ 4 }}}\)
\(51 = 80 - 4! - 5 \)
\(52 = \frac{ 8 }{ 4 } + 50 \)
\(53 = 40 + 5 + 8 \)
\(54 = 50 - 4 + 8 \)
\(55 = 8^{0} + 54 \)
\(56 = 50 - \sqrt{4} + 8 \)
\(57 = 58 - 4^{0 }\)
\(58 = 0 \cdot 4 + 58 \)
\(59 = 4^{0} + 58 \)
\(60 = \sqrt{450 \cdot 8 }\)
\(61 = 54 - 0! + 8 \)
\(62 = 50 + 4 + 8 \)
\(63 = \frac{ 504 }{ 8 }\)
\(64 = \frac{ 40 }{ 5 } \cdot 8 \)
\(65 = \sqrt{\sqrt{5^{8}}} + 40 \)
\(66 = 50 + 4! - 8 \)
\(67 = \frac{ 5! }{ \sqrt{4} } - 0! + 8 \)
\(68 = 80 - \sqrt{4! + 5 !}\)
\(69 = 8^{0 + \sqrt{4}} + 5 \)
\(70 = 80 - \sqrt{4} \cdot 5 \)
\(71 = 80 - 4 - 5 \)
\(72 = 5! - 40 - 8 \)
\(73 = 80 - \sqrt{4} - 5 \)
\(74 = ( 8 - 4 )! + 50 \)
\(75 = \sqrt{80^{\sqrt{4}}} - 5 \)
\(76 = \sqrt{( 4 - 0! )^{8}} - 5 \)
\(77 = 80 + \sqrt{4} - 5 \)
\(78 = 84 - 0! - 5 \)
\(79 = 80 + 4 - 5 \)
\(80 = \frac{ 8! }{ 504 }\)
\(81 = 80 - 4 + 5 \)
\(82 = 4 \cdot 8 + 50 \)
\(83 = 84 - 5^{0 }\)
\(84 = 0 \cdot 5 + 84 \)
\(85 = 5^{0} + 84 \)
\(86 = 4^{0} + 85 \)
\(87 = 80 + \sqrt{4} + 5 \)
\(88 = 5! - 40 + 8 \)
\(89 = 80 + 4 + 5 \)
\(90 = \sqrt{4} \cdot 5 + 80 \)
\(91 = ( 4 - 0! )! + 85 \)
\(92 = 50 \cdot \sqrt{4} - 8 \)
\(93 = \frac{ ( 0! + 5 )! + 4! }{ 8 }\)
\(94 = \frac{ ( 0! + 5 )! }{ 8 } + 4 \)
\(95 = \sqrt{0! + 5!} + 84 \)
\(96 = \frac{ 480 }{ 5 }\)
\(97 = 5! - ( 4! - 8^{0 } )\)
\(98 = 40 + 58 \)
\(99 = 80 + 4! - 5 \)
\(100 = \frac{ 50 \cdot 8 }{ 4 }\)