\mnb150ÿ{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\froman\fprq2 Times New Roman;}{\f4\fswiss\fprq2 Arial;}{\f5\fnil Courier Neu;}{\f6\fmodern\fprq1 Courier New;}{\f7\fmodern Courier New;}{\f8\froman Times New Roman;}{\f9\froman\fprq2 Symbol;}{\f10\froman\fcharset1 Times New Roman;}{\f11\froman\fprq2\fcharset2 Symbol;}} {\colortbl\red0\green0\blue0;\red255\green0\blue0;\red0\green0\blue255;\red0\green128\blue0;\red0\green255\blue0;} \deflang1031\pard\ri4\plain\f4\fs40\cf0 Periodische Kommazahlen \par \plain\f4\fs24\cf0 Mathematik mit MuPAD: Prof. Dr. D\'f6rte Haftendorn, Mai 2004 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}DIGITS:=40 //Dezimalen-Anzeige vergr\'f6\'dfern \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw776\pich827\picwgoal439\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}float(1/17) \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw9348\pich825\picscalex99\picscaley99\picwgoal5300\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect \par \pard\ri4\plain\f4\fs24\cf0 So kann man die Periodenl\'e4nge ablesen. \par \plain\f4\fs24\cf0\b Experimentiere mit 1/n , wie lang ist jeweils die Periode?\plain\f6\fs22\cf0\b \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}n:=13: [1/n,float(1/n)] \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw10529\pich1134\picwgoal5969\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect \par \pard\ri4\plain\f4\fs24\cf0 Versuche abbbrechende und nicht abbrechende Kommazahlen zu sortieren. \par \plain\f4\fs24\cf0\b Bei welchen Nennern n bricht die Kommazahl 1/n ab?\plain\f6\fs22\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}n:=2^3*5^7: [1/n,float(1/n)] \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw4179\pich1134\picwgoal2369\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}//-------------------------------------------------------- \par \pard\ri4\plain\f4\fs24\cf0\b Experimentiere: bei welchen Nennern n erh\'e4lt man echte Vorperioden?\plain\f4\fs24\cf0 \par Vorperioden sind hinter dem Komma Ziffern ungleich Null, die nicht in der Periode vorkommen \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs24\cf0 {\pntext\f1\'b7\tab}n:=16*17: [1/n,float(1/n)]\plain\f6\fs22\cf0 \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw10952\pich1134\picwgoal6209\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab} \par {\pntext\f1\'b7\tab}//------------------------------------------------------- \par \pard\ri4\plain\f4\fs32\cf0 R\'fcckverwandlung von periodischen Kommazahlen in Br\'fcche\plain\f6\fs22\cf0 \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}DIGITS:=8: \par {\pntext\f1\'b7\tab}[1/(10^n-1),float(1/(10^n-1))] $n=1..5 \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw19024\pich1134\picwgoal10785\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}[23/(10^n-1),float(23/(10^n-1))] $n=2..5 \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw15789\pich1139\picwgoal8951\pichgoal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0000BC02000000000102022253797374656D0000040000002D010600040000002701FFFF040000 00F001000004000000F001010004000000F001020004000000F001030004000000F00104000400 00002701FFFF030000000000 }\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect \par \pard\ri4\plain\f4\fs24\cf0 Also erzeugen die Nenner mit lauter Neunen Perioden, die genau dem Z\'e4hler entsprechen, aufgef\'fcllt mit Nullen. \par Die Periodenl\'e4nge ist gleich der Anzahl der Neunen. \par Umgekehrt: \plain\f4\fs24\cf0\b F\'fcr die R\'fcckverwandlung sofort-periodischer Dezimalzahlen muss man offenbar die \par Periode als Z\'e4hler nehmen und als Nenner soviele Neunen wie die Periodenl\'e4nge angibt. \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}DIGITS:=40: \par {\pntext\f1\'b7\tab}[0.123456712345671234567,1234567/9999999,float(1234567/9999999)] \par \pard\li50\ri6\plain\f6\fs22\cf2\protect 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\pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}float(0.345+1234567/9999999000) \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw9137\pich827\picwgoal5180\pichgoal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\pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}588235294117647/9999999999999999 \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw876\pich1132\picscalex99\picscaley99\picwgoal497\pichgoal642 010009000003160100000600150000000000050000000B0200000000050000000C026C046C0303 0000001E00050000000C026E046E03050000000B0200000000030000001E00030000001E000500 00000C028302F201050000000B0200000000050000000B020000000009000000FA020000000000 00000000002200040000002D01000010000000FB0238FF00000000000090010000000107000000 417269616C000100040000002D0101000400000002010100050000000102FFFFFF00040000002E 01180005000000090200000000040000000801000015000000FB0210FF00000000000090010000 00010700000054696D6573204E657720526F6D616E000100040000002D0102000B00000026060F 000C004D617468547970650000C1000500000009020000FF00070000002105010031002301BD00 070000002105010031001C028100070000002105010037001C02F90013000000FB0210FF000000 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{\pntext\f1\'b7\tab}numlib::phi(3*11*13) \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw988\pich827\picwgoal560\pichgoal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002D010400040000002701FFFF04000000F001000004000000F001010004000000F00102000400 00002701FFFF040000002701FFFF030000000000 }\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}float(1/(2*137));float(1/(16*137)); \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw9348\pich825\picscalex99\picscaley99\picwgoal5300\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw9771\pich825\picscalex99\picscaley99\picwgoal5540\pichgoal468 0100090000030C0200000500150000000000050000000B0200000000050000000C0239032B2603 0000001E00050000000C023B032C26050000000B0200000000030000001E00030000001E000500 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}\plain\f6\fs22\cf2\protect \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}float(1/17);float(1/(16*17)); \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw9348\pich825\picscalex99\picscaley99\picwgoal5300\pichgoal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\pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}float(1/11);float(1/(4*11));float(1/(44*11)); \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw9348\pich825\picscalex99\picscaley99\picwgoal5300\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw9348\pich825\picscalex99\picscaley99\picwgoal5300\pichgoal468 010009000003FE0100000500150000000000050000000B0200000000050000000C023903842403 0000001E00050000000C023B038524050000000B0200000000030000001E00030000001E000500 00000C02D501B414050000000B0200000000050000000B020000000009000000FA020000000000 00000000002200040000002D01000010000000FB0238FF00000000000090010000000107000000 417269616C000100040000002D0101000400000002010100050000000102FFFFFF00040000002E 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}\plain\f6\fs22\cf2\protect \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}numlib::phi(44) \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw774\pich825\picscalex99\picscaley99\picwgoal439\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}DIGITS:=52 \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw774\pich825\picscalex99\picscaley99\picwgoal439\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}float(1/3);float(1/(4*3));float(1/(7*17)); \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw11676\pich825\picscalex99\picscaley99\picwgoal6620\pichgoal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00002105010033003B011018070000002105010033003B018818070000002105010033003B0100 1909000000FA02000000000000000000002200040000002D01030010000000FB02100007000000 0000BC02000000000102022253797374656D0000040000002D010400040000002701FFFF040000 00F001000004000000F001010004000000F0010200040000002701FFFF040000002701FFFF0300 00000000 }\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw11888\pich825\picscalex99\picscaley99\picwgoal6740\pichgoal468 010009000003520200000500150000000000050000000B0200000000050000000C023903702E03 0000001E00050000000C023B03712E050000000B0200000000030000001E00030000001E000500 00000C02D501541A050000000B0200000000050000000B020000000009000000FA020000000000 00000000002200040000002D01000010000000FB0238FF00000000000090010000000107000000 417269616C000100040000002D0101000400000002010100050000000102FFFFFF00040000002E 01180005000000090200000000040000000801000015000000FB0210FF00000000000090010000 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}\plain\f6\fs22\cf2\protect \par {\pict\wmetafile8\picw12098\pich825\picscalex99\picscaley99\picwgoal6859\pichgoal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}\plain\f6\fs22\cf2\protect \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}6*16 \par \pard\li600\ri1\fi-300\plain\f6\fs22\cf0 \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw774\pich825\picscalex99\picscaley99\picwgoal439\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}float(1/(11*11));float(1/(7*19));float(1/(11*17)); \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw12098\pich825\picscalex99\picscaley99\picwgoal6859\pichgoal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}\plain\f6\fs22\cf2\protect \par {\pict\wmetafile8\picw12098\pich825\picscalex99\picscaley99\picwgoal6859\pichgoal468 010009000003590200000500150000000000050000000B0200000000050000000C023903422F03 0000001E00050000000C023B03442F050000000B0200000000030000001E00030000001E000500 00000C02D501CC1A050000000B0200000000050000000B020000000009000000FA020000000000 00000000002200040000002D01000010000000FB0238FF00000000000090010000000107000000 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0000000000002200040000002D01030010000000FB021000070000000000BC0200000000010202 2253797374656D0000040000002D010400040000002701FFFF04000000F001000004000000F001 010004000000F0010200040000002701FFFF040000002701FFFF030000000000 }\plain\f6\fs22\cf2\protect \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}numlib::phi(121) \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw987\pich825\picscalex99\picscaley99\picwgoal560\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}float(1/(16*11));float(1/(4*3));float(1/(256*17)); \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw12098\pich825\picscalex99\picscaley99\picwgoal6859\pichgoal468 010009000003590200000500150000000000050000000B0200000000050000000C023903422F03 0000001E00050000000C023B03442F050000000B0200000000030000001E00030000001E000500 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010400040000002701FFFF04000000F001000004000000F001010004000000F001020004000000 2701FFFF040000002701FFFF030000000000 }\plain\f6\fs22\cf2\protect \par {\pict\wmetafile8\picw12311\pich825\picscalex99\picscaley99\picwgoal6980\pichgoal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\pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw2363\pich825\picscalex99\picscaley99\picwgoal1340\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}float(1/4);float(1/44) \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw1093\pich825\picscalex99\picscaley99\picwgoal620\pichgoal468 010009000003ED0000000500150000000000050000000B0200000000050000000C023903450403 0000001E00050000000C023B034604050000000B0200000000030000001E00030000001E000500 00000C02D5016C02050000000B0200000000050000000B020000000009000000FA020000000000 00000000002200040000002D01000010000000FB0238FF00000000000090010000000107000000 417269616C000100040000002D0101000400000002010100050000000102FFFFFF00040000002E 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19070000002105010033003B01781909000000FA02000000000000000000002200040000002D01 030010000000FB021000070000000000BC02000000000102022253797374656D0000040000002D 010400040000002701FFFF04000000F001000004000000F001010004000000F001020004000000 2701FFFF040000002701FFFF030000000000 }\plain\f6\fs22\cf2\protect \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}float(1/4);float(1/(4*17));float(1/17);float(1/34) \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw1093\pich825\picscalex99\picscaley99\picwgoal620\pichgoal468 010009000003ED0000000500150000000000050000000B0200000000050000000C023903450403 0000001E00050000000C023B034604050000000B0200000000030000001E00030000001E000500 00000C02D5016C02050000000B0200000000050000000B020000000009000000FA020000000000 00000000002200040000002D01000010000000FB0238FF00000000000090010000000107000000 417269616C000100040000002D0101000400000002010100050000000102FFFFFF00040000002E 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010009000003520200000500150000000000050000000B0200000000050000000C023903702E03 0000001E00050000000C023B03712E050000000B0200000000030000001E00030000001E000500 00000C02D501541A050000000B0200000000050000000B020000000009000000FA020000000000 00000000002200040000002D01000010000000FB0238FF00000000000090010000000107000000 417269616C000100040000002D0101000400000002010100050000000102FFFFFF00040000002E 01180005000000090200000000040000000801000015000000FB0210FF00000000000090010000 00010700000054696D6573204E657720526F6D616E000100040000002D0102000B00000026060F 000C004D6174685479706500007B000500000009020000FF00070000002105010030003B016400 07000000210501002E003B01DC00070000002105010030003B011801070000002105010033003B 019001070000002105010034003B010802070000002105010034003B0180020700000021050100 38003B01F802070000002105010032003B017003070000002105010037003B01E8030700000021 05010035003B016004070000002105010038003B01D804070000002105010036003B0150050700 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07000000210501002E003B01DC00070000002105010030003B011801070000002105010030003B 019001070000002105010030003B010802070000002105010033003B0180020700000021050100 32003B01F80209000000FA02000000000000000000002200040000002D01030010000000FB0210 00070000000000BC02000000000102022253797374656D0000040000002D010400040000002701 FFFF04000000F001000004000000F001010004000000F0010200040000002701FFFF0400000027 01FFFF030000000000 }\plain\f6\fs22\cf2\protect \par \par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f6\fs22\cf0 {\pntext\f1\'b7\tab}1/99;float(%) \par \pard\li50\ri6\plain\f6\fs22\cf2\protect {\pict\wmetafile8\picw876\pich1132\picscalex99\picscaley99\picwgoal497\pichgoal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}\plain\f6\fs22\cf2\protect \par \pard\li50\ri2\plain\f6\fs22\cf2\protect 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