Question

0.27是个循环小数，它化成分数是多少

Answer 1

解：0.2727.....
是个纯循环小数
0.27.......
0.27+0.0027.....
=0.27+0.0027+0.000027+0.00000027+....
是无穷等比数列an=a1q^(n-1)=0.27x(0.01)^(n-1),n:N*的前n项和在n-无穷大时候的极限值
a1=0.27,q=0.01,
/q/=/0.01/=0.01属于（-1，0）u(0,1)
s=a1/(1-q)=0.27/(1-0.01)=0.27/0.99=27/99=9/33=3/11
答：答案是3/11.

Answer 2

设a=0.27循环，100a=27.2727循环
100a–a=99a=27，a=27/99=3/11

Answer 3

27/99=3/11≈0.2727