EXPRESS AS A FRACTION IN LOWEST TERMS.
0.555......
0.555...... HOW CAN I EXPRESS AS A FRACTION?
數學既問題！
2006-10-18 5:21 pm
回答 (5)
2006-10-19 1:03 am
✔ 最佳答案
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
參考: 中四級數學書
2006-10-18 6:17 pm
Let X = 0.555.........
then, 10X = 5.555.....
Hence
10X - X = 5.555.... - 0.555....
9X = 5
X = 5/9
∴ 0.555.... = 5/9
then, 10X = 5.555.....
Hence
10X - X = 5.555.... - 0.555....
9X = 5
X = 5/9
∴ 0.555.... = 5/9
參考: myself
2006-10-18 5:28 pm
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
then
a=0.555................
10a=5.555................
so, 10a - a= 5.555......... - 0.555.........
9a=5
a=5/9
2006-10-18 5:27 pm
即係轉為分數
I think... = 111/200
I think... = 111/200
2006-10-18 5:25 pm
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)
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)
收錄日期: 2021-04-12 22:52:10
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061018000051KK00653