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考数根法第三小数廻环求数根法:“凡本数为法,以除一,皆成廻环不尽之小数,其廻环数有正负相间者,有有正无负者,视有几位而得廻环,以其位数代前法之定次,余如前法.”如N为素数,则1/N有N-1位循环,或为d位循环,而d/N-1;如:1/(131)有130位数字;1/(41)有(40)/8位数字;1/(37)有(36)/(12)位数字;李善兰以位数作为定次,与前二法均合.华衡芳循环小数考说:“其所谓廻环数,即循环数也,本数即分母也,定次即循环之位数也,依李氏术,似可从分母求得位数,惟言廻环数有正负相间者尚未考得.”
Examine the root of the third decimal number to find a number of roots: “Where this number is a law, in addition to one, are all indefinite decimal numbers of the ring, the ring number is positive and negative and there are positive and negative, Depending on the number of points and the order of the previous method of the number of digits, the remainder is the same as the previous method.” If N is a prime number, then 1/N has a N-1 bit cycle, or a d-bit cycle, and d /N-1; for example: 1/(131) has 130 digits; 1/(41) has (40)/8 digits; 1/(37) has (36)/(12) digits; Li Shanlan is in position Number as a fixed number, and the first two methods are equal. Huaheng Fang cycle decimal examination: "The so-called ring number, that is, the number of cycles, this number is the denominator also, the number of cycles is also set, according to Lee’s surgery , it seems that the number of digits can be obtained from the denominator.