All 100 targets have a solution.
\(1 = 98 - 97 \)
\(2 = 9 - ( 9 - 8 ) \cdot 7 \)
\(3 = 9 \cdot 9 - 78 \)
\(4 = \frac{ 78 }{ \sqrt{9}! } - 9 \)
\(5 = \frac{ 98 }{ 7 } - 9 \)
\(6 = 87 - 9 \cdot 9 \)
\(7 = 79 - 8 \cdot 9 \)
\(8 = 97 - 89 \)
\(9 = \frac{ 78 + \sqrt{9} }{ 9 }\)
\(10 = 89 - 79 \)
\(11 = \frac{ 79 + 9 }{ 8 }\)
\(12 = 99 - 87 \)
\(13 = \frac{ 99 - 8 }{ 7 }\)
\(14 = \frac{ 89 + 9 }{ 7 }\)
\(15 = 7 + 8 - 9 + 9 \)
\(16 = ( 9 - 8 ) \cdot 7 + 9 \)
\(17 = \frac{ 78 }{ \sqrt{9} } - 9 \)
\(18 = \frac{ 7 + 9 }{ 8 } \cdot 9 \)
\(19 = 98 - 79 \)
\(20 = \frac{ 87 }{ \sqrt{9} } - 9 \)
\(21 = 99 - 78 \)
\(22 = \frac{ 78 }{ \sqrt{9}! } + 9 \)
\(23 = \frac{ 98 }{ 7 } + 9 \)
\(24 = 78 - \sqrt{9}! \cdot 9 \)
\(25 = 97 - 8 \cdot 9 \)
\(26 = 89 - 7 \cdot 9 \)
\(27 = \frac{ 78 + \sqrt{9} }{ \sqrt{9 } }\)
\(28 = \frac{ 87 - \sqrt{9} }{ \sqrt{9 } }\)
\(29 = \frac{ 78 + 9 }{ \sqrt{9 } }\)
\(30 = \sqrt{897 + \sqrt{9 }}\)
\(31 = 79 - 8 \cdot \sqrt{9 }!\)
\(32 = \frac{ 87 + 9 }{ \sqrt{9 } }\)
\(33 = 7 + 8 + 9 + 9 \)
\(34 = ( 9 - 7 ) \cdot ( 8 + 9 )\)
\(35 = 98 - 7 \cdot 9 \)
\(36 = \frac{ 8 }{ 9 - 7 } \cdot 9 \)
\(37 = 8 \cdot \sqrt{9} + 7 + \sqrt{9 }!\)
\(38 = \frac{ 87 }{ \sqrt{9} } + 9 \)
\(39 = \frac{ 7^{\sqrt{9}} + 8 }{ 9 }\)
\(40 = 8 \cdot \sqrt{9} + 7 + 9 \)
\(41 = ( 8 - \sqrt{9} )! - 79 \)
\(42 = \frac{ 98 }{ 7 } \cdot \sqrt{9 }\)
\(43 = 99 - 7 \cdot 8 \)
\(44 = ( 8 - \sqrt{9} ) \cdot 7 + 9 \)
\(45 = \frac{ 7 + 8 }{ \sqrt{9} } \cdot 9 \)
\(46 = 7 \cdot 9 - 8 - 9 \)
\(47 = 89 - 7 \cdot \sqrt{9 }!\)
\(48 = ( 7 - \frac{ 9 }{ 9 } ) \cdot 8 \)
\(49 = \frac{ 98 }{ 9 - 7 }\)
\(50 = 99 - \sqrt{\sqrt{7^{8 }}}\)
\(51 = 78 - \sqrt{9} \cdot 9 \)
\(52 = \frac{ 78 \cdot \sqrt{9}! }{ 9 }\)
\(53 = 7 \cdot 8 - \frac{ 9 }{ \sqrt{9 } }\)
\(54 = ( 7 + 8 - 9 ) \cdot 9 \)
\(55 = 79 - 8 \cdot \sqrt{9 }\)
\(56 = 7 \cdot 8 - 9 + 9 \)
\(57 = 7 \cdot 8 + \frac{ 9 }{ 9 }\)
\(58 = \frac{ 87 \cdot \sqrt{9}! }{ 9 }\)
\(59 = 7 \cdot 8 + \frac{ 9 }{ \sqrt{9 } }\)
\(60 = 78 - 9 - 9 \)
\(61 = 8^{9 - 7} - \sqrt{9 }\)
\(62 = 79 - 8 - 9 \)
\(63 = \frac{ 7! }{ 89 - 9 }\)
\(64 = 7 \cdot 9 - 8 + 9 \)
\(65 = 79 - 8 - \sqrt{9 }!\)
\(66 = 78 - 9 - \sqrt{9 }\)
\(67 = 8^{9 - 7} + \sqrt{9 }\)
\(68 = 79 - 8 - \sqrt{9 }\)
\(69 = 87 - 9 - 9 \)
\(70 = 8 \cdot 9 + 7 - 9 \)
\(71 = ( 7 + \sqrt{9} ) \cdot 8 - 9 \)
\(72 = 78 - 9 + \sqrt{9 }\)
\(73 = 89 - 7 - 9 \)
\(74 = 79 - 8 + \sqrt{9 }\)
\(75 = 78 - \frac{ 9 }{ \sqrt{9 } }\)
\(76 = 89 - 7 - \sqrt{9 }!\)
\(77 = 78 - \frac{ 9 }{ 9 }\)
\(78 = 78 - 9 + 9 \)
\(79 = \frac{ 9 }{ 9 } + 78 \)
\(80 = 79 - 8 + 9 \)
\(81 = \frac{ 9 }{ \sqrt{9} } + 78 \)
\(82 = 98 - 7 - 9 \)
\(83 = 97 - 8 - \sqrt{9 }!\)
\(84 = 99 - 7 - 8 \)
\(85 = 89 - 7 + \sqrt{9 }\)
\(86 = 87 - \frac{ 9 }{ 9 }\)
\(87 = 87 - 9 + 9 \)
\(88 = \frac{ 9 }{ 9 } + 87 \)
\(89 = \sqrt{89^{9 - 7 }}\)
\(90 = 78 + \sqrt{9} + 9 \)
\(91 = 89 - 7 + 9 \)
\(92 = 97 - 8 + \sqrt{9 }\)
\(93 = 87 - \sqrt{9} + 9 \)
\(94 = 98 - 7 + \sqrt{9 }\)
\(95 = 97 - 8 + \sqrt{9 }!\)
\(96 = 78 + 9 + 9 \)
\(97 = ( 9 - 8 ) \cdot 97 \)
\(98 = 97 - 8 + 9 \)
\(99 = ( 8 - 7 ) \cdot 99 \)
\(100 = 98 - 7 + 9 \)