级数收敛意义下的一个循环小数的加法问题

Addition Problem with Recurring Decimal under the Meaning of Series Convergence

根据2011版课程标准,循环小数的认识安排在小学学习.在解决循环小数相加问题时,可能会遇到用初等数学知识难以解释的情况.例如0.33·+0.1 6·=0.4 9·的算理是什么?为什么可以通过循环节重整把0.3·改写为0.3 3·0.33 3·,0.333 3·…对类似这样的问题如果从级数收敛的意义去认识,对于用高观点理解和认识循环小数具有一定的意义.

The basic understanding of the recurring decimals is the 2011 version of the course standard. It which is difficult to explain when solving the arranged to study in primary school according to is possible to encounter with the elementary mathematics knowledge problem of recurring decimal addition, for instance, what is the calcu- lation rule for O. 3 3 ＋ 0. 1 6 = O. 4 9 .9 Why is O. 3 changed into 0. 3 30. 33 3,0. 333 3 by Circular section reforming and so on. For similar problems, if they can be understood from the meaning of the series converges , it is signifi- cant to understand and know the recurring decimals from the the high point of view.