数制转换过程中小数的“有限—无限”现象  

The "Finite to Infinite" Phenomenon in the Process of Number System Conversion

作　　者：吴菊凤[1] 陈雪梨[1] 

机构地区：[1]浙江邮电职业技术学院数学教研室,浙江绍兴312016

出　　处：《绍兴文理学院学报》2011年第7期16-19,共4页Journal of Shaoxing University

摘　　要：文章对十进制小数转换为R进制小数的方法进行了探讨,对转换方法"乘R取整法"进行了论证,当转换后是无限位的R进制小数时,则转换是极限意义上的相等.之后,文章还给出了十进制小数转换为R进制数后是循环小数的充要条件.The methods of conversing a decimal fraction to a R System number was studied in this paper,and the mechanism of method＂ taking integer part from the product with R＂ was demonstrated. When the digital number become infinite after conversing, the numbers before conversion and after conversion are equal in the sense of lim- it. Then we got a necessary and sufficient condition for a decimal fraction conversed to be a circulating decimal in R systems.

关 键 词：数制 乘R取整法 级数 收敛 循环小数 

分 类 号：O173[理学—数学]