Case 1 is best approximated as 1/1

Case 2 is best approximated as 1000000/1

Case 3 is best approximated as 833719/265381

Case 4 is best approximated as 566827/208524

Case 5 is best approximated as 10/9

Case 6 is best approximated as 965271/202705

Case 7 is best approximated as 772540/113157

Case 8 is best approximated as 859212/350975

Case 9 is best approximated as 262796/44137

Case 10 is best approximated as 111667/95978

Case 11 is best approximated as 896804/485547

Case 12 is best approximated as 417966/238439

Case 13 is best approximated as 864155/411291

Case 14 is best approximated as 633203/92016

Case 15 is best approximated as 768351/137563

Case 16 is best approximated as 796437/111575

Case 17 is best approximated as 562221/74629

Case 18 is best approximated as 618659/62777

Case 19 is best approximated as 65957/11536

Case 20 is best approximated as 959/120

Case 21 is best approximated as 663483/314989

Case 22 is best approximated as 330770/47859

Case 23 is best approximated as 165069/17557

Case 24 is best approximated as 807280/116351

Case 25 is best approximated as 339815/76017

Case 26 is best approximated as 781062/371449

Case 27 is best approximated as 655507/85377

Case 28 is best approximated as 847298/184297

Case 29 is best approximated as 808232/119157

Case 30 is best approximated as 756280/176951