2022年小学奥数之各种循环小数化成分数的方法归纳2 .pdf

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1、各种循环小数化成分数的方法归纳一、纯循环小数化分数从小数点后面第一位就循环的小数叫做纯循环小数。怎样把它化为分数呢？看下面例题。例 1 把纯循环小数化分数：从以上例题可以看出，纯循环小数的小数部分可以化成分数，这个分数的分子是一个循环节表示的数，分母各位上的数都是9。9 的个数与循环节的位数相同。能约分的要约分。二、混循环小数化分数不是从小数点后第一位就循环的小数叫混循环小数。怎样把混循环小数化为分数呢？看下面的例题。例 2 把混循环小数化分数。（2）先看小数部分 0.353 由以上例题可以看出，一个混循环小数的小数部分可以化成分数，这个分数的分子是第二个循环节以前的小数部分组成的数与小数部分

2、中不循环部分组成的数的差。分母的头几位数是9，末几位是 0。9 的个数与循环节中的位数相同，0 的个数与不循环部分的位数相同。文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U

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8、HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4三、循环小数的四则运算循环小数化成分数后，循环小数的四则运算就可以按分数四则运算法则进行。从这种意义上来讲，循环小数的四则运算和有限小数四则运算一样，也是分数的四则运算。例 3 计算下面各题：解：先把循环小数化成分数后再计算。例 4

9、计算下面各题。文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T

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13、9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T

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15、9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4分析与解：（1）把循环小数化成分数，再按分数计算。（2）可根据乘法分配律把1.25 提出，再计算。（3）把循环小数化成分数，根据乘法分配律和等差数列求和公式计算。文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4

16、T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4U9S4U3B4文档编码:CL6L3I4T7K7 HH1L4J5A8J8 ZC4

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