數學既問題！

將循環小數化為分數，可有兩種方法計，如下

方法一：
設x = 0.5 (5上面加一點，代表循環小數)
即x = 0.555... .....(1)
10x = 5.555... ....(2) ←將方程(1)乘10
(2)﹣(1)：
10x﹣9x = 5.555...﹣0.555...
9x = 5
x = 5 / 9
∴0.555...... = 5 / 9

方法二：
設x = 0.5 (5上面加一點，代表循環小數)
即10x = 5.555... ←將x = 5.555... 乘10
10x = 5 + 0.555...
10x = 5 + x
10x﹣x = 5
9x = 5
x = 5 / 9
∴0.555... = 5 / 9

Let X = 0.555.........
then, 10X = 5.555.....

Hence
10X - X = 5.555.... - 0.555....
9X = 5
X = 5/9

∴ 0.555.... = 5/9

First, we let a=0.555........

then
a=0.555................
10a=5.555................

so, 10a - a= 5.555......... - 0.555.........

9a=5

a=5/9

即係轉為分數
I think... = 111/200

let
S=0.555......
10S=5.555..........
9S=5
S=5/9
0.555......=5/9

2006-10-18 09:52:28 補充：
10*0.555...是移位問題10*0.12=1.2 (1,2向左移了一位)10*0.555...=5.5555 (每個5向左移一位)