很難呀! 快來教我! 把循環小數化分數

1.設 0.148 148 148 ... = x ,1000x - x = (148. 148 148 ...) - 0.148 148 148 ... 999x = 148x = 148/9992.設 0.5 678 678 678 ... = y ,0 .0 678 678 678 ... = y - 0.5(678 . 678 678 ... ) - (0.678 678 678 ...) = 10000(y - 0.5) - 10(y - 0.5)678 = 10000y - 5000 - 10y + 55673 = 9990yy = 5673 / 9990y = 1891 / 3330

2010-07-25 12:53:25 補充：
方法二 :
1.

0.148 148 148 ...

= 148/999

2.

0.5 678 678 678 ...

= 0.5 + 0.0 678 678 678 ...

= 1/2 + 678/9990

= 1/2 + 113/1665

= 1665/3330 + 226/3330

= 1891 / 3330

1) 148/999
2) 5673/9990


P.S.我沒有打錯字。是5673/9990 不是5678/9990

2010-07-25 15:54:44 補充：
解釋：
0.148148148148=X
1000X=148.148148148148
1000X-X=148
999X=148
X=148/999


0.5678678678=X
10000X=5678.678678678
10X=5.678678678
10000X-10X=5673
9990X=5673
X=5673/9990
=1891/3330

1) 0.148 = 14.8%
2) 0.5678 = 56.78%

將小數點向右移兩位及加上符號「%」

例1: 0.278 = 27.8%
例2: 1.201 = 120.1%

2010-07-25 12:28:14 補充：
1) 0.148 = 14.8% = 14.8/100 = 6.7/25

2) 0.5678 = 56.78% = 56.78/100 = 28.39/50

將百分數寫成分母為100的分,並化簡!!