无限循环小数与分数之间的互化

2025-06-28 19:40:51
推荐回答(2个)
回答1:

哈哈,就是1
可以看成是一个无穷等比数列0.9,0.09,0.009,0.0009,......的和

0.9999999999999999999......=0.9/(1-0.1)=1

首项为a1,公比为q(|q|<=1)无穷等比数列的和S=a1/(1-q)

回答2:

设A=0.9999999999999...
则:10A = 9.9999999999999999999
则: 10A-A = 9A = 9
得:A=1
即: 0.999999999999... = 1