Exhaustive list (*) of fractions that use all digits as their decimal values. -with all digits from 1 to 9, each used only once ...exactly as a SUDOKU puzzle..., 2 solutions: 124983/576 = 216.984375 8954631/72 = 124369.875 -with all digits from 0 to 9, each used only once, 5 solutions: 2340819/576 = 4063.921875 <- sent in my previous message 2409183/576 = 4182.609375 4023189/576 = 6984.703125 4138209/576 = 7184.390625 4309281/576 = 7481.390625 576 = 2^6 * 3^2 is the preferred denominator. The only other one is 72 = 2^3 * 3^2 = 576/8. With these denominators, all the numerators are of course multiples of 3^2, avoiding infinite decimal representation. Christian. (*) "Should be" exhaustive, but an error is possible. -----Message d'origine----- De : math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com [mailto:math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com] De la part de Christian Boyer Envoyé : jeudi 21 septembre 2006 12:00 À : 'math-fun' Objet : RE: [math-fun] Decimal question Not a "reduced" fractional representation, but do you like this one? Using all digits from 0 to 9. Each once. 2340819/576 = 4063.921875 Christian. -----Message d'origine----- De : math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com [mailto:math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com] De la part de Christian Boyer Envoyé : mardi 19 septembre 2006 19:34 À : 'math-fun' Objet : RE: [math-fun] Decimal question 5/2 = 2.5 Christian. -----Message d'origine----- De : math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com [mailto:math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com] De la part de David Wilson Envoyé : mardi 19 septembre 2006 18:29 À : math-fun Objet : [math-fun] Decimal question Is there a finite decimal that uses the same digits as its reduced fractional representation?