互化
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/22 06:56:59
怎么做
![](http://img.wesiedu.com/upload/3/d9/3d96cb1225255a4c4f3b9b4484475c0c.jpg)
![](http://img.wesiedu.com/upload/3/d9/3d96cb1225255a4c4f3b9b4484475c0c.jpg)
![互化](/uploads/image/z/18490833-9-3.jpg?t=%E4%BA%92%E5%8C%96)
解题思路: 根据上式加数的特点,分别差0.1,0.01,0.001,0.0001…0.0000000001就等于1,所以故假设都等于1,所以算式的结果是10,再用10减去0.1,0.01,0.001…0.0000000001的和,所以最后的结果是10-0.1111111111,计算后可得到答案。
解题过程:
9/10+99/100+999/1000+...+9999999999/10000000000
=(1+1+1+1+1+1+1+1+1+1)-(0.1+0.01+0.01+…+0.0000000001),
=10-0.1111111111,
=9.8888888889,
答:原式的和的整数部分是9.
解题过程:
9/10+99/100+999/1000+...+9999999999/10000000000
=(1+1+1+1+1+1+1+1+1+1)-(0.1+0.01+0.01+…+0.0000000001),
=10-0.1111111111,
=9.8888888889,
答:原式的和的整数部分是9.