0.45轉1成最簡單分數 b分a
更新1:
係循環小數0.45454545454545....................
循環小數化分數
回答 (2)
2006-10-23 1:12 am
✔ 最佳答案
let x=0.4545454545...........(1)100x=45.454545454545.......(2)
(2)-(1)=100x-x=45.454545...-0.454545.....
99x=45
x=5/11
2006-10-23 1:20 am
如果要將一個循環小數轉化為分數
設該循環小數為N=0.abcdef......nabcdef......nabcdef......
設由a到n共有y個數
10^y N=abcdef......n.abcdef......nabcdef......
10^y N-N=abcdef......n
(10^y-1)N=abcdef......n
N=abcdef......n/(10^y-1)
在N=0.454545......的情況下
y=2
故N=45/(10^2-1)=45/99=5/11
設該循環小數為N=0.abcdef......nabcdef......nabcdef......
設由a到n共有y個數
10^y N=abcdef......n.abcdef......nabcdef......
10^y N-N=abcdef......n
(10^y-1)N=abcdef......n
N=abcdef......n/(10^y-1)
在N=0.454545......的情況下
y=2
故N=45/(10^2-1)=45/99=5/11
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061022000051KK03709