1. 0.99999…=0.111111……×9=1／9×9=1
2. 用除法竖式1÷1=1
1÷1=0.999999……
1=0.***********……
求证方法还有很多,不止这两种!
1:0.9999....*9=9.9999....-0.9999....=9,
0.9999....*9=9,0.9999....=1
2:1-0.9999....=0.0....01,
由上得0.0....01=0,
0.9999....=1-0=1.
一、因为 0.333333....=1/3
0.333333....*3=0.999999....
又因为 1/3*3=1
所以0.999999....=1
二、设X=0.999999...①
则10X=9.999999...②
②-①得
9X=9
X=1
所以
1＝0.9999......
证一：0.9999999......=0.9+0.09+...+0.00...09+...=0.9/(1-0.1)=1
证二：0.999999......=9*0.11...1...=9*(1/9)=1